A B\"ocherer-Type Conjecture for Paramodular Forms
Number Theory
2010-06-09 v1
Abstract
In the 1980s B\"ocherer formulated a conjecture relating the central value of the quadratic twists of the spinor L-function attached to a Siegel modular form F to the coefficients of F . He proved the conjecture when F is a Saito-Kurokawa lift. Later Kohnen and Kuss gave numerical evidence for the conjecture in the case when F is a rational eigenform that is not a Saito-Kurokawa lift. In this paper we develop a conjecture relating the central value of the quadratic twists of the spinor L-function attached to a paramodular form and the coefficients of the form. We prove the conjecture in the case when the form is a Gritsenko lift and provide numerical evidence when it is not a lift.
Keywords
Cite
@article{arxiv.1006.1582,
title = {A B\"ocherer-Type Conjecture for Paramodular Forms},
author = {Nathan C. Ryan and Gonzalo Tornaría},
journal= {arXiv preprint arXiv:1006.1582},
year = {2010}
}