We obtain sharp upper and lower bounds on a certain four-dimensional Frobenius number determined by a prime pair (p,q), 2\lt p\lt q, including exact formulae for two infinite subclasses of such pairs. The problem is motivated by the study of compact (Riemann) surfaces which can be realized as 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. The general n-dimensional Frobenius problem (for n \geq 3) is NP-hard, and it may be that our restricted problem retains this property. (Joint work with Cormac O'Sullivan, BCC, CUNY)
Anthony Weaver