A converse theorem for quasimodular forms-Reference-Cited by-同舟云学术

A converse theorem for quasimodular forms

Published:2022-03-01 Issue:2 Volume:34 Page:547-564
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Charan Mrityunjoy¹,Meher Jaban¹,Shankhadhar Karam Deo²,Singh Ranveer Kumar³

Affiliation:

1. School of Mathematical Sciences , National Institute of Science Education and Research , Bhubaneswar , HBNI, P.O. Jatni, Khurda 752050, Odisha , India

2. Department of Mathematics , Indian Institute of Science Education and Research Bhopal , Bhopal Bypass Road, Bhauri , Bhopal 462 066, Madhya Pradesh , India

3. NHETC , Department of Physics and Astronomy , Rutgers University , 126 Frelinghuysen Rd. , Piscataway NJ 08855 , USA

Abstract

Abstract In this paper, we consider twisted Dirichlet series attached to quasimodular forms, study their analytic properties, and prove an analogue of Weil’s converse theorem for quasimodular forms over congruence subgroups. We also give some applications of our results to a certain q-series and sign changes of the Fourier coefficients of quasimodular forms.

Funder

Science and Engineering Research Board

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2021-0241/pdf

Reference14 articles.

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3. H. Cohen and F. Strömberg, Modular Forms: A Classical Approach, Grad. Stud. Math. 179, American Mathematical Society, Providence, 2017.

4. E. Hecke, Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann. 112 (1936), no. 1, 664–699.

5. H. Jacquet and R. P. Langlands, Automorphic Forms on GL⁢(2){\rm GL}(2), Lecture Notes in Math. 114, Springer, Berlin, 1970.

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