Rojas León, AntonioWan, Daqing2016-06-082016-06-082011-10Rojas León, A. y Wan, D. (2011). Improvements of the Weil bound for Artin-Schreier curves. Mathematische Annalen, 351 (2), 417-442.0025-58311432-1807http://hdl.handle.net/11441/42021For 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/s00208-010-0606-3