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arXiv:math/0603358 [math.NT]AbstractReferencesReviewsResources

On the representation of integers by quadratic forms

T. D. Browning, R. Dietmann

Published 2006-03-14, updated 2006-12-12Version 2

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.

Comments: 33 pages
Categories: math.NT
Subjects: 11D72, 11D09, 11P55
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