On binary correlations of Fourier coefficients of holomorphic cusp forms at prime arguments

2025/11/13 by Kim, Jiseong, Nath, Kunjakanan
#11F30 #11N37 #11P55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.10594

Abstract

Let \λ_f(n)\_{n ≥ 1} be the normalized Hecke eigenvalues of a given holomorphic cusp form f of even weight k. We show under the assumption of the existence of Littlewood's type zero free region for L(s, f, χ), where χ is a Dirichlet character modulo q, that if X^2/3+ε ≪ H ≪ X^1-ε with ε>0, then for any A≥ 1, ∑_{1≤ |h|≤ H}| ∑_\substackX

Related

• Triple correlations of Fourier coefficients of cusp forms
• Correlations of multiplicative functions with automorphic L-functions
• Large sums of Hecke eigenvalues of holomorphic cusp forms
• Monotone chains of Fourier coefficients of Hecke cusp forms
• Dissipation of correlations of holomorphic cusp forms