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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2010, Issue 638


On Katz's bound for the number of elements with given trace and norm

Marko Moisio
  • Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland. e-mail:
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/ Daqing Wan
Published Online: 2009-11-23 | DOI: https://doi.org/10.1515/crelle.2010.002


In this note an improvement of Katz's bound on the number of elements in a finite field with given trace and norm is given. The improvement is obtained by reducing the problem to estimating the number of rational points on certain toric Calabi-Yau hypersurfaces, and then to use detailed cohomological calculations by Rojas-Leon and the second author for such toric hypersurfaces.

About the article

Received: 2008-02-21

Published Online: 2009-11-23

Published in Print: 2010-01-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2010, Issue 638, Pages 69–74, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2010.002.

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