2006•arXiv (Cornell University)Open access

On the representation of integers by quadratic forms

T. D. Browning, Rainer Dietmann

Abstract

Let Q be a non-singular quadratic form with integer coefficients. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q=0. When Q is positive definite we provide improved upper bounds for the least positive integer k such that the equation Q=k is insoluble in integers, despite being soluble modulo every prime power.

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Key concepts: Integer (computer science), Mathematics, Modulo, Quadratic equation, Quadratic integer, Prime power, Prime (order theory), Representation (politics)