%0 Journal Article
%T A Diophantine Frobenius problem related to Riemann surfaces
%A Cormac O'Sullivan
%A Anthony Weaver
%J Mathematics
%D 2009
%I arXiv
%X We obtain sharp upper and lower bounds on a certain four-dimensional Frobenius number determined by a prime pair $(p,q)$, $2<p<q$, including exact formulae for two infinite subclasses of such pairs. Our work is motivated by the study of compact Riemann surfaces which can be realized as a semi-regular $pq$-fold coverings of surfaces of lower genus. In this context, the Frobenius number is (up to an additive translation) the largest genus in which no surface is such a covering. In many cases it is also the largest genus in which no surface admits an automorphism of order $pq$. The general $t$-dimensional Frobenius problem ($t \geq 3$) is $NP$-hard, and it may be that our restricted problem retains this property.
%U http://arxiv.org/abs/0912.2513v1