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On products of Fourier coefficients of half-integral weight cusp forms

Abhishek Juyal and Manish Kumar Pandey

Vol. 13 (2024), No. 2, 93–101
Abstract

We investigate the nonvanishing properties of shifted products af(n)af(n + r), n 1, for a fixed positive integer r. The focus is on Fourier coefficients associated with half-integral weight modular forms. This study serves as an extension of work of Hofmann and Kohnen (Forum Math. 29:1 (2017), 245–250).

Keywords
cusp forms, Fourier coefficients, half-integral weight, $L$-function
Mathematical Subject Classification
Primary: 11F12, 11F30
Secondary: 11F37
Milestones
Received: 22 June 2023
Revised: 14 February 2024
Accepted: 1 March 2024
Published: 22 March 2024
Authors
Abhishek Juyal
Department of Mathematics
Hemvati Nandan Bahuguna Garhwal University (A Central University)
BCC Campus Srinagar
Uttarakhand
India
Manish Kumar Pandey
Department of Mathematics
UPES
Uttarakhand
India