Kloosterman sums and Fourier coefficients of Eisenstein series

TL;DR

This paper derives explicit formulas for Kloosterman sums on (N) and Fourier coefficients of Eisenstein series at arbitrary cusps, advancing understanding of automorphic forms and their arithmetic properties.

Contribution

It provides new explicit formulas for Kloosterman sums and Fourier coefficients of Eisenstein series at general Atkin-Lehner cusps, extending previous results.

Findings

Explicit formulas for Kloosterman sums on (N).

Explicit formulas for Fourier coefficients of Eisenstein series at arbitrary cusps.

Enhanced tools for studying automorphic forms and their arithmetic properties.

Abstract

We derive explicit formulas for some Kloosterman sums on $\Gamma_0(N)$, and for the Fourier coefficients of Eisenstein series attached to arbitrary cusps, around a general Atkin-Lehner cusp.