English

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 LL-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}
}