Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection
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- by Ben Kane and Sudhir Pujahari
- Trans. Amer. Math. Soc. 376 (2023), 5503-5519
- DOI: https://doi.org/10.1090/tran/8885
- Published electronically: May 23, 2023
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Abstract:
In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix $t$ in an arithmetic progression $t\equiv m\ \, \left ( \operatorname {mod} \, M \right )$ and consider the ratio of the $2k$-th moment to the zeroeth moment for $H(4n-t^2)$ as one varies $n$. The special case $n=p^r$ yields as a consequence asymptotic formulas for moments of the trace $t\equiv m\ \, \left ( \operatorname {mod} \, M \right )$ of Frobenius on elliptic curves over finite fields with $p^r$ elements.References
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Bibliographic Information
- Ben Kane
- Affiliation: Department of Mathematics, University of Hong Kong, Pokfulam, Hong Kong
- MR Author ID: 789505
- ORCID: 0000-0003-4074-7662
- Email: bkane@hku.hk
- Sudhir Pujahari
- Affiliation: School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, An OCC of Homi Bhabha National Institute, P. O. Jatni, Khurda 752050, Odisha, India
- MR Author ID: 1101430
- Email: spujahari@niser.ac.in; spujahari@gmail.com
- Received by editor(s): June 19, 2022
- Received by editor(s) in revised form: December 6, 2022
- Published electronically: May 23, 2023
- Additional Notes: The research of the first author was supported by grants from the Research Grants Council of the Hong Kong SAR, China (project numbers HKU 17301317, and 17303618). Most of the research was conducted while the second author was a postdoctoral fellow at The University of Hong Kong. He thanks the university for providing excellent facilities and a productive environment and would also like to thank the Institute of Mathematical Research at the University of Hong Kong for providing partial financial assistance to the postdoctoral fellowship.
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 5503-5519
- MSC (2020): Primary 11E41, 11F27, 11F37, 11G05
- DOI: https://doi.org/10.1090/tran/8885
- MathSciNet review: 4630752