The Mordell integral, quantum modular forms, and mock Jacobi forms

It is explained how the Mordell integral ∫ R e πiτ x 2 − 2 πzx cosh ( πx ) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q -hypergeometric series and mock and partial theta fu...

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Bibliographic Details
Published inResearch in number theory Vol. 1; no. 1
Main Authors Chern, Bobbie, Rhoades, Robert C
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2015
Subjects
Mathematics
Mathematics and Statistics
Number Theory
Research Article
Mordell integral
False theta function
Ramanujan
Partial theta function
Mock theta function
Jacobi forms
mock Jacobi Form
partial Jacobi theta function
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Summary:It is explained how the Mordell integral ∫ R e πiτ x 2 − 2 πzx cosh ( πx ) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q -hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z . Mathematics Subject Classification: 11P55, 05A17
ISSN:2363-9555
2363-9555
DOI:10.1007/s40993-015-0002-x