Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-24T23:45:51.289Z Has data issue: false hasContentIssue false

A FROBENIUS QUESTION RELATED TO ACTIONS ON CURVES IN CHARACTERISTIC P

Published online by Cambridge University Press:  13 August 2013

DARREN B. GLASS*
Affiliation:
Department of Mathematics, Gettysburg College, Gettysburg, PA 17325, USA e-mail: dglass@gettysburg.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider which integers g can occur as the genus and of a curve defined over a field of characteristic p which admits an automorphism of degree pq, where p and q are distinct primes. This investigation leads us to consider a certain family of three-dimensional Frobenius problems and prove explicit formulas giving their solution in many cases.

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Byrnes, J. S., On a partition problem of Frobenius, J. Comb. Theory Ser. A 17 (1974), 162166. MR 0347732 (50 #234).CrossRefGoogle Scholar
2.Curtis, F., On formulas for the Frobenius number of a numerical semigroup, Math. Scand. 67 (2) (1990), 190192. MR 1096454 (92e:11019).Google Scholar
3.Glass, D., The 2-ranks of hyperelliptic curves with extra automorphisms, Int. J. Number Theory 5 (5) (2009), 897910. MR 2553515 (2010h:11100).CrossRefGoogle Scholar
4.Glass, D., Non-genera of curves with automorphisms in characteristic p, in Computational algebraic and analytic geometry, Contemporary Mathematics, vol. 572 (Seppälä, M. and Volcheck, E., Editors) (American Mathematical Society, Providence RI, 2012), 8995.CrossRefGoogle Scholar
5.O'Sullivan, C. and Weaver, A., A diophantine frobenius problem related to Riemann surfaces, Glasg. Math. J. 53 (3) (2011), 501522. MR 2822795.Google Scholar
6.Sylvester, J. J., Question 7382, in Mathematical questions from the educational times, vol. 41 (1884).Google Scholar