English

On the representation of integers by quadratic forms

Number Theory 2014-02-26 v2

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.

Keywords

Cite

@article{arxiv.math/0603358,
  title  = {On the representation of integers by quadratic forms},
  author = {T. D. Browning and R. Dietmann},
  journal= {arXiv preprint arXiv:math/0603358},
  year   = {2014}
}

Comments

33 pages

R2 v1 2026-07-22T17:32:54.871Z