The Fifth Moment of modular L-functions

Abstract

We prove a sharp bound on the fifth moment of modular L-functions of fixed small weight, and large prime level.

v1: 81 pages. v3: 65 pages. We have extracted some material which now appears in two shorter, stand-alone papers. The calculations of Kloosterman sums and Fourier coefficients of Eisenstein series are in one new paper, and the stationary phase results are in a new paper with Ian Petrow as an additional co-author. This version also implements minor corrections and improvements to exposition

References in corpus (2)

• Oscillatory integrals with uniformity in parameters
• A generalized cubic moment and the Petersson formula for newforms

Cited by in corpus (2)

• The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound
• Short Second Moment Bound for GL(2) $L$-functions in $q$-Aspect