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

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.

arXiv commentWe added some examples

References in corpus (1)

• On the lifting of Hilbert cusp forms to Hilbert-Siegel cusp forms

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