L Polynomials of the Curve yqn y xqh 1 over Fqm

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2014-09-28

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Özbudak, Ferruh

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Let chi be a smooth, geometrically irreducible and projective curve over a finite field F-q of odd characteristic. The L-polynomial L-chi(t) of chi determines the number of rational points of chi not only over F-q but also over F-qs for any integer s >= 1. In this paper we determine L-polynomials of a class of such curves over F-q.

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https://hdl.handle.net/11511/82631

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L Polynomials of the Curve yqn y xqh 1 over Fqm, Aithmetic of Finite Fields, Kocaeli, Türkiye, 27 - 28 Eylül 2014

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L-Polynomials of the Curve Özbudak, Ferruh (2014-09-28) Let chi be a smooth, geometrically irreducible and projective curve over a finite field F-q of odd characteristic. The L-polynomial L-chi(t) of chi determines the number of rational points of chi not only over F-q but also over F-qs for any integer s >= 1. In this paper we determine L-polynomials of a class of such curves over F-q.
REGULARITY OF QUOTIENTS OF DRINFELD MODULAR SCHEMES Kondo, Satoshi; Yasuda, Seidai (Mathematical Sciences Publishers, 2020-02-01) Let A be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal I subset of A, Drinfeld defined the notion of structure of level I on a Drinfeld module.
Finite type points on subsets of C-n Yazıcı, Özcan (Elsevier BV, 2020-07-01) In [4], D'Angelo introduced the notion of points of finite type for a real hypersurface M subset of C-n and showed that the set of points of finite type in M is open. Later, Lamel-Mir [8] considered a natural extension of D'Angelo's definition for an arbitrary set M subset of C-n. Building on D'Angelo's work, we prove the openness of the set of points of finite type for any subset M subset of C-n.
Value sets of Lattes maps over finite fields Küçüksakallı, Ömer (Elsevier BV, 2014-10-01) We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
Some maximal function fields and additive polynomials GARCİA, Arnaldo; Özbudak, Ferruh (Informa UK Limited, 2007-01-01) We derive explicit equations for the maximal function fields F over F-q(2n) given by F = F-q(2n) (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field F-q(2n), and where A(Y) is q- additive and deg(f) = q(n) + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over F-q(2n) (i.e., the extension H/F is Galois).

Citation Formats

F. Özbudak, “L Polynomials of the Curve yqn y xqh 1 over Fqm,” presented at the L Polynomials of the Curve yqn y xqh 1 over Fqm, Aithmetic of Finite Fields, Kocaeli, Türkiye, 27 - 28 Eylül 2014, Kocaeli, Türkiye, 2014, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/82631.