Refined upper bounds for the linear Diophantine problem of Frobenius

Details Refined upper bounds for the linear Diophantine problem of Frobenius Refined upper bounds for the linear Diophantine problem of Frobenius

2003-05-29

arxiv.org/abs/math/0305420v2

Adv. Appl. Math. 32, no. 3 (2004), 454-467

Mathematics

Number Theory

12 pages, 5 figures

Scientific paper

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.

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