Explicit class number formulas for Siegel–Weil averages of ternary quadratic forms
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- by Ben Kane, Daejun Kim and Srimathi Varadharajan;
- Trans. Amer. Math. Soc. 376 (2023), 1625-1652
- DOI: https://doi.org/10.1090/tran/8814
- Published electronically: December 8, 2022
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Abstract:
In this paper, we investigate the interplay between positive-definite integral ternary quadratic forms and class numbers. We generalize a result of Jones relating the theta function for the genus of a quadratic form to the Hurwitz class numbers, obtaining an asymptotic formula (with a main term and error term away from finitely many bad square classes $t_j\mathbb {Z}^2$) relating the number of lattice points in a quadratic space of a given norm with a sum of class numbers related to that norm and the squarefree part of the discriminant of the quadratic form on this lattice.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
- Daejun Kim
- Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, Korea
- MR Author ID: 1423067
- ORCID: 0000-0003-3203-1648
- Email: dkim01@kias.re.kr
- Srimathi Varadharajan
- Affiliation: Department of Mathematics, University of Hong Kong, Pokfulam, Hong Kong
- MR Author ID: 1319947
- Email: srimathi1388@gmail.com
- Received by editor(s): March 30, 2022
- Received by editor(s) in revised form: July 13, 2022
- Published electronically: December 8, 2022
- Additional Notes: Ben Kane and Daejun Kim are the corresponding authors
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). This work of the second author was supported by Basic Science Research Program through NRF funded by the Minister of Education (NRF-2020R1A6A3A03037816) while his staying at HKU as an honorary research associate, and by a KIAS Individual Grant (MG085501) at Korea Institute for Advanced Study. - © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 1625-1652
- MSC (2020): Primary 11E20, 11E41, 11H55
- DOI: https://doi.org/10.1090/tran/8814
- MathSciNet review: 4549687