Journal of the Ramanujan Mathematical Society

Volume 40, Issue 2, June 2025 pp. 177–203.

On average behavior of Fourier coefficients of certain Rankin-Selberg L-functions over the values of a multivariate polynomial and its consequences

Authors: Anubhav Sharma, Ayyadurai Sankaranarayanan and Huafeng Liu
Author institution:Department of Mathematics, Indian Institute of Technology Bombay, Mumbai 400 076, Maharashtra, India.

Summary: In this paper, we establish the asymptotic formulae for the first and second moments of Fourier coefficients of the automorphic L-functions L(s, f ⊗ f ⊗ f) and L(s, f ⊗ f ⊗ f ⊗ g) attached to the primitive holomorphic cusp forms f and g (distinct) of weights k{1} and k{2}, respectively, for the full modular group S L(2; ℤ) over the values of a multivariate polynomial. As a consequence, we also provide the quantitative results for the number of sign changes of these Fourier coefficients over the same sequence in the interval (x; 2x] for sufficiently large x.

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