On the coefficients of symmetric power L-functions

2017/03/24 by Jaban Meher, Meher, Jaban, Karam Deo Shankhadhar +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1703.08344

openalex publication_date 2017/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the signs of the Fourier coefficients of a newform. Let f be a normalized newform of weight k for Γ₀(N). Let a_f(n) be the nth Fourier coefficient of f. For any fixed positive integer m, we study the distribution of the signs of \a_f(p^m)\_p, where p runs over all prime numbers. We also find out the abscissas of absolute convergence of two Dirichlet series with coefficients involving the Fourier coefficients of cusp forms and the coefficients of symmetric power L-functions.

Cited by

• Effective Joint Sato-Tate Distribution and Sign Change of Symmetric Power Coefficients

Related

• Higher symmetric power L-functions and their Fourier coefficients
• On the average behavior of the Fourier coefficients of j^th symmetric power L-function over a certain sequences of positive integers
• Sign changes in Fourier coefficients of the symmetric power L-functions on sums of two squares
• Fourier Coefficients Of Some Cusp Forms
• The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms