The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy

We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell fun...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Mortenson, Eric T. [verfasserIn] Zwegers, Sander [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Appell functions Theta functions Indefinite theta series Hecke-type double-sums Mock modular forms Quantum modular forms

Übergeordnetes Werk:	Enthalten in: Advances in mathematics - Amsterdam [u.a.] : Elsevier, 1961, 418
Übergeordnetes Werk:	volume:418

DOI / URN:	10.1016/j.aim.2023.108944

Katalog-ID:	ELV009428801

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245	1	0	\|a The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy
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520			\|a We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots.
650		4	\|a Appell functions
650		4	\|a Theta functions
650		4	\|a Indefinite theta series
650		4	\|a Hecke-type double-sums
650		4	\|a Mock modular forms
650		4	\|a Quantum modular forms
700	1		\|a Zwegers, Sander \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Advances in mathematics \|d Amsterdam [u.a.] : Elsevier, 1961 \|g 418 \|h Online-Ressource \|w (DE-627)268759200 \|w (DE-600)1472893-X \|w (DE-576)103373292 \|x 1090-2082 \|7 nnns
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936	b	k	\|a 31.00 \|j Mathematik: Allgemeines
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allfields	10.1016/j.aim.2023.108944 doi (DE-627)ELV009428801 (ELSEVIER)S0001-8708(23)00087-7 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Mortenson, Eric T. verfasserin aut The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots. Appell functions Theta functions Indefinite theta series Hecke-type double-sums Mock modular forms Quantum modular forms Zwegers, Sander verfasserin aut Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 418 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:418 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 418
spelling	10.1016/j.aim.2023.108944 doi (DE-627)ELV009428801 (ELSEVIER)S0001-8708(23)00087-7 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Mortenson, Eric T. verfasserin aut The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots. Appell functions Theta functions Indefinite theta series Hecke-type double-sums Mock modular forms Quantum modular forms Zwegers, Sander verfasserin aut Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 418 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:418 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 418
allfields_unstemmed	10.1016/j.aim.2023.108944 doi (DE-627)ELV009428801 (ELSEVIER)S0001-8708(23)00087-7 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Mortenson, Eric T. verfasserin aut The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots. Appell functions Theta functions Indefinite theta series Hecke-type double-sums Mock modular forms Quantum modular forms Zwegers, Sander verfasserin aut Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 418 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:418 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 418
allfieldsGer	10.1016/j.aim.2023.108944 doi (DE-627)ELV009428801 (ELSEVIER)S0001-8708(23)00087-7 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Mortenson, Eric T. verfasserin aut The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots. Appell functions Theta functions Indefinite theta series Hecke-type double-sums Mock modular forms Quantum modular forms Zwegers, Sander verfasserin aut Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 418 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:418 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 418
allfieldsSound	10.1016/j.aim.2023.108944 doi (DE-627)ELV009428801 (ELSEVIER)S0001-8708(23)00087-7 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Mortenson, Eric T. verfasserin aut The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots. Appell functions Theta functions Indefinite theta series Hecke-type double-sums Mock modular forms Quantum modular forms Zwegers, Sander verfasserin aut Enthalten in Advances in mathematics Amsterdam [u.a.] : Elsevier, 1961 418 Online-Ressource (DE-627)268759200 (DE-600)1472893-X (DE-576)103373292 1090-2082 nnns volume:418 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 418
language	English
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topic_facet	Appell functions Theta functions Indefinite theta series Hecke-type double-sums Mock modular forms Quantum modular forms
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container_title	Advances in mathematics
authorswithroles_txt_mv	Mortenson, Eric T. @@aut@@ Zwegers, Sander @@aut@@
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author	Mortenson, Eric T.
spellingShingle	Mortenson, Eric T. ddc 510 bkl 31.00 misc Appell functions misc Theta functions misc Indefinite theta series misc Hecke-type double-sums misc Mock modular forms misc Quantum modular forms The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy
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topic_title	510 DE-600 31.00 bkl The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy Appell functions Theta functions Indefinite theta series Hecke-type double-sums Mock modular forms Quantum modular forms
topic	ddc 510 bkl 31.00 misc Appell functions misc Theta functions misc Indefinite theta series misc Hecke-type double-sums misc Mock modular forms misc Quantum modular forms
topic_unstemmed	ddc 510 bkl 31.00 misc Appell functions misc Theta functions misc Indefinite theta series misc Hecke-type double-sums misc Mock modular forms misc Quantum modular forms
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title	The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy
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title_full	The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy
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title_sort	the mixed mock modularity of certain duals of generalized quantum modular forms of hikami and lovejoy
title_auth	The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy
abstract	We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots.
abstractGer	We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots.
abstract_unstemmed	We resolve a question of Hikami and Lovejoy that sits at the intersection of quantum modular forms, mock modular forms, and knot theory. We express a family of Hecke–Appell-type sums of Hikami and Lovejoy in terms of mixed mock modular forms; in particular, we express the sums in terms of Appell functions and theta functions. They obtained their family of Hecke–Appell-type sums by considering certain duals of generalized quantum modular forms, where the quantum modular forms are motivated by the colored Jones polynomial for special torus knots.
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title_short	The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy
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up_date	2024-07-06T23:07:36.460Z
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The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy

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