English

Vector-valued Eisenstein series of small weight

Number Theory 2018-09-28 v2

Abstract

We study the (mock) Eisenstein series EkE_k of weight k{1,3/2,2}k \in \{1,3/2,2\} for the Weil representation on an even lattice, defined as the result of Bruinier and Kuss's coefficient formula for the Eisenstein series naively evaluated at kk. We describe the transformation law of EkE_k in general. Most of this note is dedicated to collecting examples where the coefficients of EkE_k contain interesting arithmetic information. Finally we make a few remarks about the case k=1/2k=1/2.

Keywords

Cite

@article{arxiv.1706.03738,
  title  = {Vector-valued Eisenstein series of small weight},
  author = {Brandon Williams},
  journal= {arXiv preprint arXiv:1706.03738},
  year   = {2018}
}

Comments

21 pages. v2 expands the discussion for the weight 1/2 series, adds more references and examples and makes several minor changes

R2 v1 2026-06-22T20:16:34.634Z