Article
Improvements of the Weil bound for Artin-Schreier curves
Author/s | Rojas León, Antonio
Wan, Daqing |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2011-10 |
Deposit Date | 2016-06-08 |
Published in |
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Abstract | For the Artin-Schreier curve y q − y = f(x) defined over a finite field Fq of q elements, the celebrated Weil bound for the number of Fq r -rational
points can be sharp, especially in super-singular cases and when r is ... For the Artin-Schreier curve y q − y = f(x) defined over a finite field Fq of q elements, the celebrated Weil bound for the number of Fq r -rational points can be sharp, especially in super-singular cases and when r is divisible. In this paper, we show how the Weil bound can be significantly improved, using ideas from moment L-functions and Katz’s work on l-adic monodromy calculations. Roughly speaking, we show that in favorable cases (which happens quite often), one can remove an extra √q factor in the error term. |
Project ID. | P08-FQM-03894
MTM2007-66929 |
Citation | Rojas León, A. y Wan, D. (2011). Improvements of the Weil bound for Artin-Schreier curves. Mathematische Annalen, 351 (2), 417-442. |
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