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

Abstract

In this paper, we give a formula for the extended Gross-Keating datum of a quadratic form defined over a finite extension of ${\mathbb{Z}}_p$ (for $p>2$) or a finite unramified extension of ${\mathbb{Z}}_2$. As an application, we describe an explicit formula for the Siegel series for ${\mathbb{Z}}_p$. We also present the details of algorithms implemented in a Mathematica package to compute the extended Gross-Keating datum and the Siegel series.

32 pages

References in corpus (5)

• Class polynomials for nonholomorphic modular functions
• Group schemes and local densities of quadratic lattices in residue characteristic 2
• Using Katsurada's Determination of the Eisenstein Series to Compute Siegel Eigenforms
• A reformulation of the Siegel series and intersection numbers
• On the local density formula and the Gross-Keating invariant with an Appendix `The local density of a binary quadratic form' by T. Ikeda and H. Katsurada

Cited by in corpus (1)

• On the local density formula and the Gross-Keating invariant with an Appendix `The local density of a binary quadratic form' by T. Ikeda and H. Katsurada