Summation formulas for Hurwitz class numbers and other mock modular coefficients
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866912367170813952 |
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| author | Beckwith, Olivia Diamantis, Nikolaos Gupta, Rajat Rolen, Larry Thalagoda, Kalani |
| author_facet | Beckwith, Olivia Diamantis, Nikolaos Gupta, Rajat Rolen, Larry Thalagoda, Kalani |
| contents | We prove a formula for weighted sums of the first $n$ coefficients of mock modular forms of moderate growth and apply it to Hurwitz class numbers and coefficients of negative half integral weight Eisenstein series, which take the form of certain quadratic Dirichlet $L$-values. Our formula is a mock modular version of a Bessel-sum identity proved by Chandrasekharan and Narasimhan for Dirichlet series satisfying a functional equation. Our proof utilizes $L$-functions for mock modular Eisenstein series defined by Shankadhar and Singh. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Summation formulas for Hurwitz class numbers and other mock modular coefficients Beckwith, Olivia Diamantis, Nikolaos Gupta, Rajat Rolen, Larry Thalagoda, Kalani Number Theory We prove a formula for weighted sums of the first $n$ coefficients of mock modular forms of moderate growth and apply it to Hurwitz class numbers and coefficients of negative half integral weight Eisenstein series, which take the form of certain quadratic Dirichlet $L$-values. Our formula is a mock modular version of a Bessel-sum identity proved by Chandrasekharan and Narasimhan for Dirichlet series satisfying a functional equation. Our proof utilizes $L$-functions for mock modular Eisenstein series defined by Shankadhar and Singh. |
| title | Summation formulas for Hurwitz class numbers and other mock modular coefficients |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.05574 |