Applications of Kronecker's limit formula for elliptic Eisenstein series
Number Theory
2015-05-13 v1
Abstract
We develop two applications of the Kronecker's limit formula associated to elliptic Eisenstein series: A factorization theorem for holomorphic modular forms, and a proof of Weil's reciprocity law. Several examples of the general factorization results are computed, specifically for certain moonshine groups, congruence subgroups, and, more generally, non-compact subgroups with one cusp. In particular, we explicitly compute the Kronecker limit function associated to certain elliptic points for a few small level moonshine groups.
Keywords
Cite
@article{arxiv.1505.02812,
title = {Applications of Kronecker's limit formula for elliptic Eisenstein series},
author = {Jay Jorgenson and Anna-Maria von Pippich and Lejla Smajlovic},
journal= {arXiv preprint arXiv:1505.02812},
year = {2015}
}