On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line
Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Tam, D. D. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Anmerkung: |
© Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Acta mathematica hungarica - Dordrecht [u.a.] : Springer Science + Business Media B.V., 1950, 170(2023), 1 vom: Juni, Seite 110-149 |
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| Übergeordnetes Werk: |
volume:170 ; year:2023 ; number:1 ; month:06 ; pages:110-149 |
| Links: |
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| DOI / URN: |
10.1007/s10474-023-01348-0 |
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| Katalog-ID: |
SPR052274454 |
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| 520 | |a Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. | ||
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10.1007/s10474-023-01348-0 doi (DE-627)SPR052274454 (SPR)s10474-023-01348-0-e DE-627 ger DE-627 rakwb eng Tam, D. D. verfasserin aut On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. Enthalten in Acta mathematica hungarica Dordrecht [u.a.] : Springer Science + Business Media B.V., 1950 170(2023), 1 vom: Juni, Seite 110-149 (DE-627)312806000 (DE-600)2012194-5 1588-2632 nnns volume:170 year:2023 number:1 month:06 pages:110-149 https://dx.doi.org/10.1007/s10474-023-01348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 170 2023 1 06 110-149 |
| spelling |
10.1007/s10474-023-01348-0 doi (DE-627)SPR052274454 (SPR)s10474-023-01348-0-e DE-627 ger DE-627 rakwb eng Tam, D. D. verfasserin aut On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. Enthalten in Acta mathematica hungarica Dordrecht [u.a.] : Springer Science + Business Media B.V., 1950 170(2023), 1 vom: Juni, Seite 110-149 (DE-627)312806000 (DE-600)2012194-5 1588-2632 nnns volume:170 year:2023 number:1 month:06 pages:110-149 https://dx.doi.org/10.1007/s10474-023-01348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 170 2023 1 06 110-149 |
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10.1007/s10474-023-01348-0 doi (DE-627)SPR052274454 (SPR)s10474-023-01348-0-e DE-627 ger DE-627 rakwb eng Tam, D. D. verfasserin aut On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. Enthalten in Acta mathematica hungarica Dordrecht [u.a.] : Springer Science + Business Media B.V., 1950 170(2023), 1 vom: Juni, Seite 110-149 (DE-627)312806000 (DE-600)2012194-5 1588-2632 nnns volume:170 year:2023 number:1 month:06 pages:110-149 https://dx.doi.org/10.1007/s10474-023-01348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 170 2023 1 06 110-149 |
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10.1007/s10474-023-01348-0 doi (DE-627)SPR052274454 (SPR)s10474-023-01348-0-e DE-627 ger DE-627 rakwb eng Tam, D. D. verfasserin aut On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. Enthalten in Acta mathematica hungarica Dordrecht [u.a.] : Springer Science + Business Media B.V., 1950 170(2023), 1 vom: Juni, Seite 110-149 (DE-627)312806000 (DE-600)2012194-5 1588-2632 nnns volume:170 year:2023 number:1 month:06 pages:110-149 https://dx.doi.org/10.1007/s10474-023-01348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 170 2023 1 06 110-149 |
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10.1007/s10474-023-01348-0 doi (DE-627)SPR052274454 (SPR)s10474-023-01348-0-e DE-627 ger DE-627 rakwb eng Tam, D. D. verfasserin aut On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. Enthalten in Acta mathematica hungarica Dordrecht [u.a.] : Springer Science + Business Media B.V., 1950 170(2023), 1 vom: Juni, Seite 110-149 (DE-627)312806000 (DE-600)2012194-5 1588-2632 nnns volume:170 year:2023 number:1 month:06 pages:110-149 https://dx.doi.org/10.1007/s10474-023-01348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 170 2023 1 06 110-149 |
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Tam, D. D. |
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Tam, D. D. On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line |
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On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line |
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on the distribution of zeros of linear combinations of dirichlet %$l%$-functions on the critical line |
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On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line |
| abstract |
Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. © Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. © Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract Let %$\chi%$ be a primitive Dirichlet character. Let %$\varepsilon%$ be an arbitrary positive number. We study the distribution of zeros of the function G(t)=a1Z(t,χ1)+a2Z(t,χ2)%$G(t)=a_1Z(t,\chi_1)+a_2Z(t,\chi_2)%$,where %$a_1,a_2%$ are real numbers and %$Z (t, \chi)%$ is an analogue of the Hardy function corresponding to the Dirichlet %$L%$-function. Let %$X%$ be a sufficiently large parameter. Our goal is to prove a lower bound for the number of zeros of %$G (t)%$ lying in the interval %$[T, T + H]%$ , %$H=O(\exp(\exp(\sqrt{\log\log T})))%$, which is correct for almost all %$T%$ in the interval %$[X,X+X^{\alpha}]%$ and %$0.9<\alpha<1%$. © Akadémiai Kiadó, Budapest, Hungary 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line |
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https://dx.doi.org/10.1007/s10474-023-01348-0 |
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10.1007/s10474-023-01348-0 |
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D.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the distribution of zeros of linear combinations of Dirichlet %$L%$-functions on the critical line</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Akadémiai Kiadó, Budapest, Hungary 2023. 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