A unified approach to Rohrlich-type divisor sums
Abstract
We propose a systematic method for analyzing Rohrlich-type divisor sums for arbitrary congruence subgroups 0(N). 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 N, (3) an explicit version of the theorem by Bringmann-Kane-L\"obrich-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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.