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arXiv 2008.008502020-08-03math.NT

Explicit Result on Equivalence of Rational Quadratic Forms Avoiding Primes

Wai Kiu Chan, Haochen Gao, Han Li

备注：: 12 pages

英文摘要：

Given a pair of regular quadratic forms over $\mathbb{Q}$ which are in the same genus and a finite set of primes $P$, we show that there is an effective way to determine a rational equivalence between these two quadratic forms which are integral over every prime in $P$. This answers one of the principal questions posed by Conway and Sloane in their book {\em Sphere packings, lattices and groups}, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Vol 290, Springer-Verlag, New York, 1999; page 402.

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