Special values of symmetric power L-functions and Hecke eigenvalues

2006/09/08 by Emmanuel Royer, Jie Wu, Royer, Emmanuel +1
Mathematics · #05A15 #11F12 #11F25 #11F67 #11M41 #11N36 #11N37 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0609227

openalex publication_date 2006/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the moments of L-functions of symmetric powers of modular forms at the edge of the critical strip, twisted by the central value of the L-functions of modular forms. We show that, in the case of even powers, it is equivalent to twist by the value at the edge of the critical strip of the symmetric square L-functions. We deduce information on the size of symmetric power L-functions at the edge of the critical strip under conditions. In a second part, we study the distribution of small and large Hecke eigenvalues. We deduce information on the simultaneous extremality conditions on the values of L-functions of symmetric powers of modular forms at the edge of the critical strip.

Related

• Distribution of Values of Symmetric power L-functions at the Edge of the Critical Strip
• The first moment of central values of symmetric square L-functions in the weight aspect
• Sign changes in Fourier coefficients of the symmetric power L-functions on sums of two squares
• Boundedness of denominators of special values of the L-functions for modular forms
• Twisted second moment of modular L-functions to a fixed modulus