Small zeros of quadratic forms mod P^m

Hakami, Ali H.

doi:10.12988/imf.2013.13034

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2015

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“…Using the method of exponential sums Hakami [10] generalized Cochrane's method to find a nonzero solution of (2) with max |x i | p for n 4 when m = p 2 and Q(x) is nonsingular (modp). The optimal bound, max |x i | p for n 1, was obtained by Cochrane and Hakami (using geometric method) [7].…”

Section: Introductionmentioning

confidence: 99%

Small solutions for system of homogenous polynomials congruences over a Dedekind domain

Hakami¹

2015

ijcms

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Let f 1 (x),. .. , f k (x) be homogeneous polynomials in n variables over the ring of integers R in a number field, and let A be a nonzero ideal in R. In [1], Cochrane generalized the geometric idea of Schinzel, Schlickewei and Schmidt used it in [15] to obtain small solutions to the system of congruences f 1 (x) ≡ • • • ≡ f k (x) ≡ 0 (mod A), the notation of a small point being given two interpretations, a point having coordinates with small norms, and a point having coordinates of small size. In this paper, we shall follow [1] and [15] to find small solutions of the above system over a Dedekind domain.

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Section: Introductionmentioning

confidence: 99%