A unified approach to Rohrlich-type divisor sums
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929546675093504 |
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| author | Jeon, Daeyeol Kang, Soon-Yi Kim, Chang Heon Matsusaka, Toshiki |
| author_facet | Jeon, Daeyeol Kang, Soon-Yi Kim, Chang Heon Matsusaka, Toshiki |
| contents | We propose a systematic method for analyzing Rohrlich-type divisor sums for arbitrary congruence subgroups $Γ_0(N)$. 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-Löbrich-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A unified approach to Rohrlich-type divisor sums Jeon, Daeyeol Kang, Soon-Yi Kim, Chang Heon Matsusaka, Toshiki Number Theory 11F25, 11F37 We propose a systematic method for analyzing Rohrlich-type divisor sums for arbitrary congruence subgroups $Γ_0(N)$. 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-Löbrich-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. |
| title | A unified approach to Rohrlich-type divisor sums |
| topic | Number Theory 11F25, 11F37 |
| url | https://arxiv.org/abs/2410.12571 |