Curves with many points and configurations of hyperplanes over finite fields

We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.


Curves related to Coulter's maximal curves
ÇAKÇAK, Emrah; Özbudak, Ferruh (Elsevier BV, 2008-01-01)
We study a class of curves over finite fields such that the maximal (respectively minimal) curves of this class form a subclass containing the set of maximal (respectively minimal) curves of Coulter (cf. [R.S. Coulter, The number of rational points of a class of Artin-Schreier curves, Finite Fields Appl. 8 (2002) 397-413, Theorem 8.12]) as a proper subset. We determine the exact number of rational points of the curves in the class and we characterize maximal (respectively minimal) curves of the class as sub...
A note on divisor class groups of degree zero of algebraic function fields over finite fields
Özbudak, Ferruh (Elsevier BV, 2003-01-01)
We give tight upper bounds on the number of degree one places of an algebraic function field over a finite field in terms of the exponent of a natural subgroup of the divisor class group of degree zero.. (C) 2002 Elsevier Science (USA). All rights reserved.
Fibre products of Kummer covers and curves with many points
Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-10-01)
We study the general fibre product of any two Kummer covers of the projective line over finite fields. Under some assumptions, we obtain an involved condition for the existence of rational points in the fibre product over a rational point of the projective line so that we determine the exact number of the rational points. Using this, we construct explicit examples of such fibre products with many rational points. In particular we obtain a record and a new entry for the table (
Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
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.
Citation Formats
F. Özbudak, “Curves with many points and configurations of hyperplanes over finite fields,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 436–449, 1999, Accessed: 00, 2020. [Online]. Available: