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

Tamotsu Ikeda; Hidenori Katsurada

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arXiv · 1602.06617

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

Tamotsu Ikeda·Hidenori Katsurada

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Abstract

Let F be a non-archimedian local field of characteristic 0, and O the ring of integres 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.

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Tamotsu Ikeda, Hidenori Katsurada. 2016-02-22. An explicit formula for the Siegel series of a quadratic form over a non-archimedian local field. https://arxiv.org/abs/1602.06617

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