On a q-deformation of modular forms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Guo, Victor J. W.¹  Zudilin, Wadim² 

[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China

[2] Radboud Univ Nijmegen, IMAPP, Dept Math, POB 9010, NL-6500 GL Nijmegen, Netherlands

关键词: Ramanujan;    q-Analogue;    Cyclotomic polynomial;    Basic hypergeometric function;    (Super)congruence;   

DOI  :  10.1016/j.jmaa.2019.03.035

来源: Elsevier

【 摘 要 】

There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work, such partial sums are related to the radial asymptotics of infinite q-hypergeometric sums at roots of unity. Here we combine the two features to construct a hypergeometric q-deformation of two CM modular forms of weight 3 and discuss the corresponding q-congruences. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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