Primitive solutions of nonscalar quadratic Diophantine equations

摘要

There is a mapping of the set of primitive integral representations of a quadratic form in n - 1 variables by a quadratic form in n variables into the set of primitive representations of a rational number by a quadratic form in n variables. Such a correspondence was introduced by Shimura in 2004. The purpose of this paper is to study the former representations by describing the inverse image of the latter set under that map. As an application we discuss some specific Fourier coefficients of theta series of degree n - 1. (C) 2019 Elsevier Inc. All rights reserved.