On the distribution of the Fourier coefficients over two sparse sequences

2025/09/08 by Kampamolla, Venkatasubbareddy
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.07037

Abstract

Let j≥ 3 be any fixed integer and f be a primitive holomorphic cusp form of even integral weight κ≥ 2 for the full modular group SL(2,ℤ). We write λ_\rmsym^j f(n) for the n^th normalized Fourier coefficient of L(s,\rmsym^j f). In this article, we establish asymptotic formulae for the discrete sums of the Fourier coefficients λ_\rmsym^j f²(n) over two sparse sequence of integers, which can be written as the sum of four integral squares and the sum of six integral squares, with refined error terms.

Citations

• On the average behavior of the Fourier coefficients of j^th symmetric power L-function over a certain sequences of positive integers
• Symmetric power functoriality for holomorphic modular forms, II
• On the Rankin–Selberg problem
• Symmetric power functoriality for holomorphic modular forms
• Identities Involving Coefficients of Automorphic L-Functions
• On sums of Fourier coefficients of cusp forms
• Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions

Related

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• Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes
• On some estimates involving Fourier coefficients of Maass cusp forms