Algebraic functions over finite fields
نویسندگان
چکیده
منابع مشابه
Partial Zeta Functions of Algebraic Varieties over Finite Fields
Motivated by arithmetic applications, we introduce the notion of a partial zeta function which generalizes the classical zeta function of an algebraic variety defined over a finite field. We then explain two approaches to the general structural properties of the partial zeta function in the direction of the Weil type conjectures. The first approach, using an inductive fibred variety point of vi...
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This survey gives a concrete and intuitively self-contained introduction to the theory of pure L-functions arising from a family of algebraic varieties defined over a finite field of characteristic p. The standard fundamental questions in any theory of L-functions include the meromorphic continuation, functional equation, Riemann hypothesis (RH for short), order of zeros at special points and t...
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The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. The algorithm consists essentially of Gauss’ upper triangular form algorithm. It is proved that the basis of the ideal of algebraic relations found by the algorithm consists of polynomials having coefficie...
متن کاملWorkshop on Algebraic Curves Over Finite Fields
Let L(t) = 1+a1t+ · · ·+a2gt be the numerator of the zeta function of an algebraic curve C defined over the finite field Fq of genus g. We show that the coefficients ar of L(t) satisfy certain inequalities. Conversely, for any integers a1, . . . , am satisfying these inequalities and all sufficiently large integers g there exist curves of genus g, whose L-polynomial satisfies the following cong...
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Article history: Received 6 April 2013 Received in revised form 23 January 2014 Accepted 25 January 2014 Available online xxxx Communicated by Igor Shparlinski MSC: 11L40 05C75 05C50
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1967
ISSN: 0021-8693
DOI: 10.1016/0021-8693(67)90061-0