Computation of Gross-Keating invariants

2018/09/27 by Lee, Chul-hee
#11E08 #11E95 #11F46 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.10323

Abstract

The Gross-Keating invariant of a half-integral matrix over a p-adic integer ring is a fundamental concept in the study of quadratic forms, and has important applications to Siegel modular forms and arithmetic geometry. We introduce the Mathematica package computeGK, a computer program for calculating the Gross-Keating invariant and the Siegel series of a half-integral matrix over ℤ_p, as well as other related quantities. As a by-product, we obtain a table of the arithmetic intersection numbers related to the classical modular polynomials using the explicit formula of Gross and Keating.

Related

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• An explicit formula for the extended Gross-Keating datum of a quadratic form
• Siegel modular forms of degree two and three and invariant theory