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Asymptotic formula for shifted convolution sums involving the coefficients of an L-function

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 September 2025

Naveen K. Godara Open the ORCID record for Naveen K. Godara [Opens in a new window] ,
Anuj Jakhar  and
Kotyada Srinivas
Naveen K. Godara*
Affiliation:
Department of Mathematics, Indian Institute of Technology (IIT) Madras , Chennai 600036, Tamil Nadu, India e-mail: anujjakhar@iitm.ac.in
Anuj Jakhar
Affiliation:
Department of Mathematics, Indian Institute of Technology (IIT) Madras , Chennai 600036, Tamil Nadu, India e-mail: anujjakhar@iitm.ac.in
Kotyada Srinivas
Affiliation:
Department of Mathematics, Indian Institute of Science Education and Research Tirupati , Tirupati 517619, Andhra Pradesh, India e-mail: srini@imsc.res.in
*
e-mail: naveen.iiserb@gmail.com
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Abstract

Let $f $ be a normalized Hecke eigenform of even weight $k \geq 2$ for $SL_2(\mathbb {Z})$. In this article, we establish an asymptotic formula for the shifted convolution sum of a general divisor function, where the sum involves the Fourier coefficients of a multi-folded L-function weighted with a kernel function.

Keywords

Eigenformsautomorphic L-functionsshifted sum

MSC classification

Primary: 11F11: Holomorphic modular forms of integral weight 11F30: Fourier coefficients of automorphic forms 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 69 , Issue 1 , March 2026 , pp. 236 - 255
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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