Kloosterman sums and Fourier coefficients of Eisenstein series

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.

This material originally appeared in the first version of our preprint arXiv:1701.07507, The fifth moment of modular $L$-functions

References in corpus (1)

• Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method

Cited by in corpus (6)

• The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound
• Motohashi's fourth moment identity for non-archimedean test functions and applications
• Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications
• Quantum Unique Ergodicity for Eisenstein Series in the Level Aspect
• Chowla and Sarnak Conjectures for Kloosterman Sums
• Kloosterman sums do not correlate with periodic functions