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Abstract
We investigate the nonvanishing properties of shifted products
a f ( n ) a f ( 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
© 2024 MSP (Mathematical Sciences
Publishers).