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Weierstrass Points and Curves Over Finite Fields
Author(s) -
Stöhr KarlOtto,
Voloch José Felipe
Publication year - 1986
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-52.1.1
Subject(s) - mathematics , embedding , finite field , algebraic curve , upper and lower bounds , pure mathematics , algebraic number , order (exchange) , sequence (biology) , field (mathematics) , discrete mathematics , mathematical analysis , finance , artificial intelligence , biology , computer science , economics , genetics
For any projective embedding of a non‐singular irreducible complete algebraic curve defined over a finite field, we obtain an upper bound for the number of its rational points. The constants in the bound are related to the Weierstrass order‐sequence associated with the projective embedding. The bounds obtained lead to a proof of the Riemann hypothesis for curves over finite fields and yield several improvements on it.