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arXiv · 1809.10323

Computation of Gross-Keating invariants

Chul-hee Lee
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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 $\mathbb{Z}_p$, 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.

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Chul-hee Lee. 2018-09-27. Computation of Gross-Keating invariants. https://arxiv.org/abs/1809.10323

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