Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T00:26:53.037Z Has data issue: false hasContentIssue false
  • English
  • Français

Hermite’s Constant for Function Fields

Published online by Cambridge University Press:  20 November 2018

Chris Hurlburt  and
Jeffrey Lin Thunder
Chris Hurlburt
Affiliation:
Center for Communications Research, 4320 Westerra Court, San Diego, CA, 92121 USA email: [email protected]
Jeffrey Lin Thunder
Affiliation:
Dept. of Mathematics, Northern Illinois University, DeKalb, IL 60115 USA email: [email protected]
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 formulate an analog of Hermite's constant for function fields over a finite field and state a conjectural value for this analog. We prove our conjecture in many cases, and prove slightly weaker results in all other cases.

Keywords

11G5011G35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 2 , 16 April 2012 , pp. 301 - 317
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Bombieri, E. and Vaaler, J. On Siegel's lemma. Invent. Math. 73(1983), no. 1, 11–32. http://dx.doi.org/10.1007/BF01393823 Google Scholar
[2] Conway, J. H. and Sloane, N. J. A., Sphere Packings, Lattices and Groups. Grundlehren der Mathematischen Wissenschaften 290. Springer-Verlag, New York, 1991.Google Scholar
[3] Evertse, J.-H. and Schlikewei, H. P., The absolute subspace theorem and linear equations with unknowns from a multiplicative group. In: Number Theory in Progress. De Gruyter, Berlin, 1999, pp. 121–142.Google Scholar
[4] Hurlburt, C. and Thunder, J. L., Non-linear codes from points of bounded height. Finite Fields Appl. 13(2007), no. 2, 281–292. http://dx.doi.org/10.1016/j.ffa.2005.11.001 Google Scholar
[5] Roy, D. and Thunder, J. L., An absolute Siegel's lemma. J. Reine Angew. Math. 476(1996), 1–26.Google Scholar
[6] Thunder, J. L., An adelic Minkowski-Hlawka theorem and an application to Siegel's lemma. J. Reine Angew. Math. 475(1996), 167–185. http://dx.doi.org/10.1515/crll.1996.475.167 Google Scholar
[7] Thunder, J. L., Siegel's lemma for function fields. Michigan Math. J. 42(1995), no. 1, 147–162. http://dx.doi.org/10.1307/mmj/1029005160 Google Scholar
[8] Weil, A. Basic Number Theory. Third edition. Die Grundlehren der Mathematischen Wissenschaften 144. Springer-Verlag, New York, 1974.Google Scholar