L-series of Eisenstein series vanishing at critical values
Number Theory
2024-04-10 v2
Abstract
Using the relations between rational functions and Eisenstein series, as well as the inferences for cotangent sums and period polynomials, we work out a precise description for Eisenstein series whose -series vanish at certain critical values. This is possible for small weights compared to the level of the Eisenstein series. For large weights we give a partial result and determine subspaces with simultaneous vanishing properties.
Keywords
Cite
@article{arxiv.2401.08230,
title = {L-series of Eisenstein series vanishing at critical values},
author = {Johann Franke},
journal= {arXiv preprint arXiv:2401.08230},
year = {2024}
}