On a Frobenius problem for polynomials

DOI10.1216/RMJ-2017-47-5-1427zbMATH Open1431.11042arXiv1409.4129MaRDI QIDQ2409607

Yanyan Li

Publication date: 12 October 2017

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Abstract: We extend the famous diophantine Frobenius problem to the case of polynomials over a field $k$. Similar to the classical problem, we show that the $n=2$ case of the Frobenius problem for polynomials is easy to solve. In addition, we translate a few results from the Frobenius problem over $mathbbZ$ to $k[t]$ and give an algorithm to solve the Frobenius problem for polynomials over a field $k$ of sufficiently large size.

Full work available at URL: https://arxiv.org/abs/1409.4129

zbMATH Keywords

polynomialsFrobenius problemarithmetic of function fields

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Matrices, determinants in number theory (11C20) The Frobenius problem (11D07)

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