An explicit formula for the Siegel series of a quadratic form over a non-archimedean local field-Reference-Cited by-同舟云学术

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

Published:2021-12-02 Issue:783 Volume:2022 Page:1-47
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Ikeda Tamotsu¹,Katsurada Hidenori²

Affiliation:

1. Graduate School of Mathematics , Kyoto University , Kitashirakawa , Kyoto , 606-8502 , Japan

2. Muroran Institute of Technology , 27-1 Mizumoto , Muroran , 050-8585 , Japan

Abstract

Abstract Let F be a non-archimedean local field of characteristic 0, and 𝔬

{{\mathfrak{o}}}

the ring of integers in F. We give an explicit formula for the Siegel series of a half-integral matrix over 𝔬

{{\mathfrak{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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2021-0061/pdf

Reference37 articles.

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