On the representation of integers by quadratic forms

Details On the representation of integers by quadratic forms On the representation of integers by quadratic forms

2006-03-14

arxiv.org/abs/math/0603358v2

Mathematics

Number Theory

33 pages

Scientific paper

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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