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Improvements of the Weil bound for Artin-Schreier curves

 

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Opened Access Improvements of the Weil bound for Artin-Schreier curves
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Author: Rojas León, Antonio
Wan, Daqing
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2011-10
Published in: Mathematische Annalen, 351 (2), 417-442.
Document type: Article
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 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.
Cite: Rojas León, A. y Wan, D. (2011). Improvements of the Weil bound for Artin-Schreier curves. Mathematische Annalen, 351 (2), 417-442.
Size: 379.5Kb
Format: PDF

URI: http://hdl.handle.net/11441/42021

DOI: http://dx.doi.org/10.1007/s00208-010-0606-3

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