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An explicit formula for the Siegel series of a quadratic form over a non-archimedean local field

  • Tamotsu Ikeda EMAIL logo and Hidenori Katsurada
Published/Copyright: December 2, 2021

Abstract

Let F be a non-archimedean local field of characteristic 0, and 𝔬 the ring of integers in F. We give an explicit formula for the Siegel series of a half-integral matrix over 𝔬. This formula expresses the Siegel series of a half-integral matrix B explicitly in terms of the Gross–Keating invariant of B and its related invariants.

Funding statement: The research was partially supported by the JSPS KAKENHI Grant Number 26610005, 24540005, 16H03919 and 17H02834. This work was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.

Acknowledgements

We would like to thank Takuya Yamauchi and Sungmun Cho for many fruitful discussions and suggestions.

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Received: 2021-06-06
Published Online: 2021-12-02
Published in Print: 2022-02-01

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