Geodesic
A DIOPHANTINE FROBENIUS PROBLEM RELATED TO RIEMANN SURFACES
Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 501-522

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DOI

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 realised 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. 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 ≥ 3) is NP-hard, and it may be that our restricted problem retains this property.
DOI : 10.1017/S0017089511000097
Mots-clés : Primary 14J50, 11D04 
O'SULLIVAN, CORMAC; WEAVER, ANTHONY. A DIOPHANTINE FROBENIUS PROBLEM RELATED TO RIEMANN SURFACES. Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 501-522. doi: 10.1017/S0017089511000097
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     title = {A {DIOPHANTINE} {FROBENIUS} {PROBLEM} {RELATED} {TO} {RIEMANN} {SURFACES}},
     journal = {Glasgow mathematical journal},
     pages = {501--522},
     year = {2011},
     volume = {53},
     number = {3},
     doi = {10.1017/S0017089511000097},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000097/}
}
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