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Ternary quadratic forms and Heegner divisors

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Abstract

In this paper, we use the Siegel–Weil formula and the Kudla’s matching principle to prove some interesting identities between representation numbers (of ternary quadratic space) and the degree of Heegner divisors.

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Acknowledgments

This paper was inspired by Kudla’s matching principle. The author thanks him for his influence. The author thanks Tonghai Yang for his good suggestion, useful discussion, and his encouragement. The author also thanks the referees for their constructive suggestions and careful listing of the typos in early version. The author is grateful to the Mathematical Science Center of Tsinghua University, for providing him a good opportunity to visit and a good research environment in the summer 2013.

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Authors and Affiliations

  1. Department of Mathematics, Northwest University, Xi’an, 710127, People’s Republic of China

    Tuoping Du

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  1. Tuoping Du
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Correspondence to Tuoping Du.

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The author was partially supported by NSFC (Nos. 71006901), NSFC (Nos. 11171141), NSFJ (Nos. BK2010007), PAPD and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No.708044), and NSFC (11326052).

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Du, T. Ternary quadratic forms and Heegner divisors. Ramanujan J 39, 61–82 (2016). https://doi.org/10.1007/s11139-015-9697-5

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  • DOI: https://doi.org/10.1007/s11139-015-9697-5

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