An explicit formula for the extended Gross-Keating datum of a quadratic form

2017/09/08 by Sungmun Cho, Tamotsu Ikeda, Cho, Sungmun +7 · 1 citation
Mathematics · #11E08 #11E95 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11E08 #msc:11E95

paper · pdf · doi:10.48550/arxiv.1709.02772

32 pages

arxiv created 2020/04/22 · arxiv updated 2020/04/23

Abstract

In this paper, we give a formula for the extended Gross-Keating datum of a quadratic form defined over a finite extension of ℤ_p (for p>2) or a finite unramified extension of ℤ₂. As an application, we describe an explicit formula for the Siegel series for ℤ_p. We also present the details of algorithms implemented in a Mathematica package to compute the extended Gross-Keating datum and the Siegel series.

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• Computation of Gross-Keating invariants

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