Test vectors and central L-values for GL(2)
Number Theory
2017-09-11 v2
Abstract
We determine local test vectors for Waldspurger functionals for GL(2), in the case where both the representation of GL(2) and the character of the degree two extension are ramified, with certain restrictions. We use this to obtain an explicit version of Waldspurger's formula relating twisted central L-values of automorphic representations on GL(2) with certain toric period integrals. As a consequence, we generalize an average value formula of Feigon and Whitehouse, and obtain some nonvanishing results.
Keywords
Cite
@article{arxiv.1310.1765,
title = {Test vectors and central L-values for GL(2)},
author = {Daniel File and Kimball Martin and Ameya Pitale},
journal= {arXiv preprint arXiv:1310.1765},
year = {2017}
}
Comments
57 pages, to appear in Algebra and Number Theory