Analytic Representations in the 3-dim Frobenius Problem
| dc.creator | Fel, Leonid G. | |
| dc.date | 2005-07-18 | |
| dc.date.accessioned | 2026-07-07T05:21:49Z | |
| dc.date.available | 2026-07-07T05:21:49Z | |
| dc.description | We consider the Diophantine problem of Frobenius for semigroup ${\sf S}({\bf d}^3)$ where ${\bf d}^3$ denotes the tuple $(d_1,d_2,d_3)$, $\gcd(d_1,d_2,d_3)=1$. Based on the Hadamard product of analytic functions we have found the analytic representation for the diagonal elements $a_{kk}({\bf d}^3)$ of the Johnson's matrix of minimal relations in terms of $d_1,d_2,d_3$. Bearing in mind the results of the recent paper this gives the analytic representation for the Frobenius number $F({\bf d}^3)$, genus $G({\bf d}^3)$ and the Hilbert series $H({\bf d}^3;z)$ for the semigroups ${\sf S}({\bf d}^3)$. This representation does complement the Curtis' theorem on the non-algebraic representation of the Frobenius number $F({\bf d}^3)$. We also give a procedure to calculate the diagonal and off-diagonal elements of the Johnson's matrix. | |
| dc.description | 16 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0507370 | |
| dc.identifier | http://arxiv.org/abs/math/0507370 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75827 | |
| dc.subject | Number Theory | |
| dc.subject | Commutative Algebra | |
| dc.subject | Primary - 11P82; Secondary - 11D04, 20M30 | |
| dc.title | Analytic Representations in the 3-dim Frobenius Problem | |
| dc.type | text |