Mock theta functions and Appell–Lerch sums

Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As...
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Gespeichert in:

Autor*in:	Chen, Bin [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Mock theta functions Bilateral series Appell–Lerch sums

Übergeordnetes Werk:	Enthalten in: Journal of inequalities and applications - Heidelberg : Springer, 2005, 2018(2018), 1 vom: 03. Juli
Übergeordnetes Werk:	volume:2018 ; year:2018 ; number:1 ; day:03 ; month:07

Links:	Volltext

DOI / URN:	10.1186/s13660-018-1748-1

Katalog-ID:	SPR032587902

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520			\|a Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications.
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allfields	10.1186/s13660-018-1748-1 doi (DE-627)SPR032587902 (SPR)s13660-018-1748-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Chen, Bin verfasserin aut Mock theta functions and Appell–Lerch sums 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications. Mock theta functions (dpeaa)DE-He213 Bilateral series (dpeaa)DE-He213 Appell–Lerch sums (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 03. Juli (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:03 month:07 https://dx.doi.org/10.1186/s13660-018-1748-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 03 07
spelling	10.1186/s13660-018-1748-1 doi (DE-627)SPR032587902 (SPR)s13660-018-1748-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Chen, Bin verfasserin aut Mock theta functions and Appell–Lerch sums 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications. Mock theta functions (dpeaa)DE-He213 Bilateral series (dpeaa)DE-He213 Appell–Lerch sums (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 03. Juli (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:03 month:07 https://dx.doi.org/10.1186/s13660-018-1748-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 03 07
allfields_unstemmed	10.1186/s13660-018-1748-1 doi (DE-627)SPR032587902 (SPR)s13660-018-1748-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Chen, Bin verfasserin aut Mock theta functions and Appell–Lerch sums 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications. Mock theta functions (dpeaa)DE-He213 Bilateral series (dpeaa)DE-He213 Appell–Lerch sums (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 03. Juli (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:03 month:07 https://dx.doi.org/10.1186/s13660-018-1748-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 03 07
allfieldsGer	10.1186/s13660-018-1748-1 doi (DE-627)SPR032587902 (SPR)s13660-018-1748-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Chen, Bin verfasserin aut Mock theta functions and Appell–Lerch sums 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications. Mock theta functions (dpeaa)DE-He213 Bilateral series (dpeaa)DE-He213 Appell–Lerch sums (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 03. Juli (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:03 month:07 https://dx.doi.org/10.1186/s13660-018-1748-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 03 07
allfieldsSound	10.1186/s13660-018-1748-1 doi (DE-627)SPR032587902 (SPR)s13660-018-1748-1-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Chen, Bin verfasserin aut Mock theta functions and Appell–Lerch sums 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications. Mock theta functions (dpeaa)DE-He213 Bilateral series (dpeaa)DE-He213 Appell–Lerch sums (dpeaa)DE-He213 Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 03. Juli (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:03 month:07 https://dx.doi.org/10.1186/s13660-018-1748-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 03 07
language	English
source	Enthalten in Journal of inequalities and applications 2018(2018), 1 vom: 03. Juli volume:2018 year:2018 number:1 day:03 month:07
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author	Chen, Bin
spellingShingle	Chen, Bin ddc 510 bkl 31.49 misc Mock theta functions misc Bilateral series misc Appell–Lerch sums Mock theta functions and Appell–Lerch sums
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topic_title	510 ASE 31.49 bkl Mock theta functions and Appell–Lerch sums Mock theta functions (dpeaa)DE-He213 Bilateral series (dpeaa)DE-He213 Appell–Lerch sums (dpeaa)DE-He213
topic	ddc 510 bkl 31.49 misc Mock theta functions misc Bilateral series misc Appell–Lerch sums
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title	Mock theta functions and Appell–Lerch sums
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title_full	Mock theta functions and Appell–Lerch sums
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title_sort	mock theta functions and appell–lerch sums
title_auth	Mock theta functions and Appell–Lerch sums
abstract	Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications.
abstractGer	Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications.
abstract_unstemmed	Abstract Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function $g_{2}{(x,q)}$. The purpose of this paper is to consider the bilateral series for the universal mock theta function $g_{3}{(x,q)}$. As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series $B(\omega;q)$ for the third order mock theta function $\omega(q)$ is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications.
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title_short	Mock theta functions and Appell–Lerch sums
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