Weighted Erdős-Kac type theorem over quadratic field in short intervals
Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Liu, Xiaoli [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© Institute of Mathematics, Czech Academy of Sciences 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Czechoslovak mathematical journal - New York, NY [u.a.] : Springer Science + Business Media B.V., 1951, 72(2022), 4 vom: 01. Sept., Seite 957-976 |
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| Übergeordnetes Werk: |
volume:72 ; year:2022 ; number:4 ; day:01 ; month:09 ; pages:957-976 |
| Links: |
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| DOI / URN: |
10.21136/CMJ.2022.0203-21 |
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| Katalog-ID: |
SPR048799866 |
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| 100 | 1 | |a Liu, Xiaoli |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Weighted Erdős-Kac type theorem over quadratic field in short intervals |
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| 520 | |a Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. | ||
| 650 | 4 | |a ideal counting function |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Erdős-Kac theorem |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a quadratic field |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a short intervals |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a mean value |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Yang, Zhishan |4 aut | |
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10.21136/CMJ.2022.0203-21 doi (DE-627)SPR048799866 (SPR)CMJ.2022.0203-21-e DE-627 ger DE-627 rakwb eng Liu, Xiaoli verfasserin aut Weighted Erdős-Kac type theorem over quadratic field in short intervals 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. ideal counting function (dpeaa)DE-He213 Erdős-Kac theorem (dpeaa)DE-He213 quadratic field (dpeaa)DE-He213 short intervals (dpeaa)DE-He213 mean value (dpeaa)DE-He213 Yang, Zhishan aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 01. Sept., Seite 957-976 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:01 month:09 pages:957-976 https://dx.doi.org/10.21136/CMJ.2022.0203-21 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_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_4012 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_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 01 09 957-976 |
| spelling |
10.21136/CMJ.2022.0203-21 doi (DE-627)SPR048799866 (SPR)CMJ.2022.0203-21-e DE-627 ger DE-627 rakwb eng Liu, Xiaoli verfasserin aut Weighted Erdős-Kac type theorem over quadratic field in short intervals 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. ideal counting function (dpeaa)DE-He213 Erdős-Kac theorem (dpeaa)DE-He213 quadratic field (dpeaa)DE-He213 short intervals (dpeaa)DE-He213 mean value (dpeaa)DE-He213 Yang, Zhishan aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 01. Sept., Seite 957-976 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:01 month:09 pages:957-976 https://dx.doi.org/10.21136/CMJ.2022.0203-21 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_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_4012 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_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 01 09 957-976 |
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10.21136/CMJ.2022.0203-21 doi (DE-627)SPR048799866 (SPR)CMJ.2022.0203-21-e DE-627 ger DE-627 rakwb eng Liu, Xiaoli verfasserin aut Weighted Erdős-Kac type theorem over quadratic field in short intervals 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. ideal counting function (dpeaa)DE-He213 Erdős-Kac theorem (dpeaa)DE-He213 quadratic field (dpeaa)DE-He213 short intervals (dpeaa)DE-He213 mean value (dpeaa)DE-He213 Yang, Zhishan aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 01. Sept., Seite 957-976 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:01 month:09 pages:957-976 https://dx.doi.org/10.21136/CMJ.2022.0203-21 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_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_4012 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_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 01 09 957-976 |
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10.21136/CMJ.2022.0203-21 doi (DE-627)SPR048799866 (SPR)CMJ.2022.0203-21-e DE-627 ger DE-627 rakwb eng Liu, Xiaoli verfasserin aut Weighted Erdős-Kac type theorem over quadratic field in short intervals 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. ideal counting function (dpeaa)DE-He213 Erdős-Kac theorem (dpeaa)DE-He213 quadratic field (dpeaa)DE-He213 short intervals (dpeaa)DE-He213 mean value (dpeaa)DE-He213 Yang, Zhishan aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 01. Sept., Seite 957-976 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:01 month:09 pages:957-976 https://dx.doi.org/10.21136/CMJ.2022.0203-21 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_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_4012 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_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 01 09 957-976 |
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10.21136/CMJ.2022.0203-21 doi (DE-627)SPR048799866 (SPR)CMJ.2022.0203-21-e DE-627 ger DE-627 rakwb eng Liu, Xiaoli verfasserin aut Weighted Erdős-Kac type theorem over quadratic field in short intervals 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute of Mathematics, Czech Academy of Sciences 2022 Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. ideal counting function (dpeaa)DE-He213 Erdős-Kac theorem (dpeaa)DE-He213 quadratic field (dpeaa)DE-He213 short intervals (dpeaa)DE-He213 mean value (dpeaa)DE-He213 Yang, Zhishan aut Enthalten in Czechoslovak mathematical journal New York, NY [u.a.] : Springer Science + Business Media B.V., 1951 72(2022), 4 vom: 01. Sept., Seite 957-976 (DE-627)327082755 (DE-600)2043740-7 1572-9141 nnns volume:72 year:2022 number:4 day:01 month:09 pages:957-976 https://dx.doi.org/10.21136/CMJ.2022.0203-21 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_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_4012 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_4367 GBV_ILN_4393 GBV_ILN_4700 AR 72 2022 4 01 09 957-976 |
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Liu, Xiaoli |
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Liu, Xiaoli misc ideal counting function misc Erdős-Kac theorem misc quadratic field misc short intervals misc mean value Weighted Erdős-Kac type theorem over quadratic field in short intervals |
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Weighted Erdős-Kac type theorem over quadratic field in short intervals ideal counting function (dpeaa)DE-He213 Erdős-Kac theorem (dpeaa)DE-He213 quadratic field (dpeaa)DE-He213 short intervals (dpeaa)DE-He213 mean value (dpeaa)DE-He213 |
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Weighted Erdős-Kac type theorem over quadratic field in short intervals |
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Weighted Erdős-Kac type theorem over quadratic field in short intervals |
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10.21136/CMJ.2022.0203-21 |
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weighted erdős-kac type theorem over quadratic field in short intervals |
| title_auth |
Weighted Erdős-Kac type theorem over quadratic field in short intervals |
| abstract |
Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. © Institute of Mathematics, Czech Academy of Sciences 2022 |
| abstractGer |
Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. © Institute of Mathematics, Czech Academy of Sciences 2022 |
| abstract_unstemmed |
Abstract Let %$\mathbb{K}%$ be a quadratic field over the rational field and %${a_\mathbb{K}}\left( n \right)%$ be the number of nonzero integral ideals with norm n. We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. We also get asymptotic formulae for the average behavior of %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ in short intervals. © Institute of Mathematics, Czech Academy of Sciences 2022 |
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Weighted Erdős-Kac type theorem over quadratic field in short intervals |
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https://dx.doi.org/10.21136/CMJ.2022.0203-21 |
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Yang, Zhishan |
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Yang, Zhishan |
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| doi_str |
10.21136/CMJ.2022.0203-21 |
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2024-07-03T21:33:04.227Z |
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We establish Erdős-Kac type theorems weighted by %${a_\mathbb{K}}{\left( n \right)^l}%$ and %${a_\mathbb{K}}{\left( {{n^2}} \right)^l}%$ of quadratic field in short intervals with l ∈ $ ℤ^{+} $. 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