Average estimates and sign change of Fourier coefficients of cusp forms at integers represented by binary quadratic form of fixed discriminant

2022/04/18 by Lalit Vaishya, Vaishya, Lalit
Mathematics · #2010 #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2204.08310

openalex publication_date 2022/04/18 · openalex created_date 2022/04/26 · openalex updated_date 2026/07/28

Abstract

In this article, we establish an average behaviour of the normalised Fourier coefficients of the Hecke eigenforms supported at the integers represented by any primitive integral positive definite binary quadratic form of fixed discriminant D < 0 when the class number h(D) = 1. We also obtain a quantitative result for the number of sign changes of the sequence of the normalised Fourier coefficients λ_f(n) of the Hecke eigenforms f where n is represented by any primitive integral positive definite binary quadratic form of fixed discriminant D < 0 when the class number h(D) = 1 in the interval (x,2x], for sufficiently large x.

Related

• First moment of Hecke eigenvalues at the integers represented by binary quadratic forms
• Non-vanishing and sign changes of Hecke eigenvalues for half-integral weight cusp forms
• Distinguishing Hecke eigenforms
• Sign Changes of Fourier Coefficients of Cusp Forms at Norm Form Arguments
• A Note On Signs Of Fourier Coefficients Of Two Cusp Forms