A unified approach to Rohrlich-type divisor sums
Number Theory
2024-10-17 v1
Abstract
We propose a systematic method for analyzing Rohrlich-type divisor sums for arbitrary congruence subgroups . Our main theorem unifies various results from the literature, and its significance is illustrated through the following five applications: (1) the valence formula, (2) a natural generalization of classical Rohrlich's formula to level , (3) an explicit version of the theorem by Bringmann-Kane-L\"{o}brich-Ono-Rolen, (4) an extension of the generalized Rohrlich formula proposed by Bringmann-Kane, and (5) an alternative proof of the decomposition formula for twisted traces of CM values of weight 0 Eisenstein series.
Cite
@article{arxiv.2410.12571,
title = {A unified approach to Rohrlich-type divisor sums},
author = {Daeyeol Jeon and Soon-Yi Kang and Chang Heon Kim and Toshiki Matsusaka},
journal= {arXiv preprint arXiv:2410.12571},
year = {2024}
}
Comments
18 pages