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

2016/02/22 by Ikeda, Tamotsu, Katsurada, Hidenori
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1602.06617

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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