Central value of automorphic L-functions

2003/01/11 by Ehud Moshe Baruch, Baruch, Ehud Moshe, Zhengyu Mao +1 · 1 citation
Mathematics · #11F37 #11F67 #11F70 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F37 #msc:11F67 #msc:11F70

paper · pdf · doi:10.48550/arxiv.math/0301115

arxiv created 2003/01/11 · arxiv updated 2009/11/30

Abstract

We prove a generalization to the totally real field case of the Waldspurger's formula relating the Fourier coefficient of a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on a new interpretation of Waldspurger's formula in terms of equality between global distributions. As applications we generalize the Kohnen-Zagier formula for holomorphic forms and prove the equivalence of the Ramanujan conjecture for half integral weight forms and a case of the Lindelof hypothesis for integral weight forms. We also study the Kohnen space in the adelic setting.

Cited by

• Gross's conjecture: the dihedral case

Related

• Waldspurger formula over function fields
• Converse theorems for automorphic distributions and Maass forms of level N
• Bhargava's composition law and Waldspurger's central value theorem
• Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg L-functions
• Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms