On Hecke eigenvalues at primes of the form $[g(n)]$

TL;DR

This paper investigates the average behavior of Fourier coefficients of holomorphic cusp forms at primes of the form [g(n)], providing insights into their distribution and properties.

Contribution

It introduces a novel analysis of Fourier coefficients at primes of specific forms, expanding understanding of their average behavior in modular forms.

Findings

Average of Fourier coefficients at primes of the form [g(n)] computed.

New bounds established for these coefficients.

Insights into the distribution of such primes and coefficients.

Abstract

In this paper, we study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form $[g(n)]$.