Refined upper bounds for the linear Diophantine problem of Frobenius

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We study the Frobenius problem: given relatively prime positive integers a_1,...,a_d, find the largest value of t (the Frobenius number g(a_1,...,a_d)) such that m_1 a_1 + ... m_d a_d = t has no solution in nonnegative integers m_1,...,m_d. We introduce a method to compute upper bounds for g(a_1,a_2,a_3), which seem to grow considerably slower than previously known bounds. Our computations are based on a formula for the restricted partition function, which involves Dedekind-Rademacher sums, and the reciprocity law for these sums.
12 pages, 5 figures

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Number Theory, Combinatorics, 11D04, 05A15, 11Y16

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http://salesiana.dossiersoluciones.com/handle/123456789/67612

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305420
 http://arxiv.org/abs/math/0305420
 Adv. Appl. Math. 32, no. 3 (2004), 454-467

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arXiv