Representations by spinor genera

John Sollion Hsia

Vol. 63 (1976), No. 1, 147–152

DOI: 10.2140/pjm.1976.63.147

Abstract

If f and g are two nonsingular quadratic forms with rational integral coefficients such that f represents g integrally over every p-adic fields and also over the reals, then it is a well-known classical result that the genus Gen (f) of f represents g. This paper considers the question of how many spinor genera in the genus of f will represent g, when f and g are integral forms defined over some fixed domain of algebraic integers and when dim(f) − dim(g) ≧ 2.

Mathematical Subject Classification

Primary: 10C05, 10C05

Milestones

Received: 14 October 1975

Published: 1 March 1976