Vector-valued Eisenstein series of small weight
Number Theory
2018-09-28 v2
Abstract
We study the (mock) Eisenstein series of weight 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 . We describe the transformation law of in general. Most of this note is dedicated to collecting examples where the coefficients of contain interesting arithmetic information. Finally we make a few remarks about the case .
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