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초록

We propose a systematic method for analyzing Rohrlich-type divisor sums for arbitrary congruence subgroups Gamma 0(N)${\Gamma }_0(N)$. 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 & ouml;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.

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