Explicit calculations with Eisenstein series
Number Theory
2020-08-17 v2
Abstract
We find explicit change-of-basis formulas between Eisenstein series attached to cusps, and newform Eisenstein series attached to pairs of primitive Dirichlet characters. As a consequence, we prove a Bruggeman-Kuznetsov formula for newforms of square-free level and trivial nebentypus. We also derive, in explicit form, the Fourier expansion, Hecke eigenvalues, Atkin-Lehner pseudo-eigenvalues, and other data associated to these Eisenstein series, with arbitrary integer weight, level, and nebentypus.
Cite
@article{arxiv.1710.03624,
title = {Explicit calculations with Eisenstein series},
author = {Matthew P Young},
journal= {arXiv preprint arXiv:1710.03624},
year = {2020}
}
Comments
37 pages. v2: implements some corrections and improvements to exposition