Refined upper bounds for the linear Diophantine problem of Frobenius
| dc.creator | Beck, Matthias | |
| dc.creator | Zacks, Shelemyahu | |
| dc.date | 2003-05-29 | |
| dc.date | 2005-01-02 | |
| dc.date.accessioned | 2026-07-07T04:58:22Z | |
| dc.date.available | 2026-07-07T04:58:22Z | |
| dc.description | 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. | |
| dc.description | 12 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0305420 | |
| dc.identifier | http://arxiv.org/abs/math/0305420 | |
| dc.identifier | Adv. Appl. Math. 32, no. 3 (2004), 454-467 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67612 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11D04, 05A15, 11Y16 | |
| dc.title | Refined upper bounds for the linear Diophantine problem of Frobenius | |
| dc.type | text |