Explicit maximal and minimal curves over finite fields of odd characteristics

In this work we present explicit classes of maximal and minimal Artin-Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1].


Knotting of algebraic curves in CP2
Finashin, Sergey (2002-01-01)
For any k⩾3, I construct infinitely many pairwise smoothly non-isotopic smooth surfaces homeomorphic to a non-singular algebraic curve of degree 2k, realizing the same homology class as such a curve and having abelian fundamental group ⧹ . This gives an answer to Problem 4.110 in the Kirby list (Kirby, Problems in low-dimensional topology, in: W. Kazez (Ed.), Geometric Topology, AMS/IP Stud. Adv. Math. vol 2.2, Amer. Math. Soc., Providence, 1997).
On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields
Özbudak, Ferruh; YAYLA, OĞUZ (2014-09-18)
We determined the number of rational points of fibre products of two Kummer covers over a rational point of the projective line in a recent work of F. Ozbudak and B. G. Temur (Des Codes Cryptogr 70(3): 385-404, 2014), where we also constructed explicit examples, including a record and two new entries for the current Table of Curves with Many Points (manYPoints: Table of curves with many points. http://www.manypoints.org (2014). Accessed 30 Sep 2014). Using the methods given in Ozbudak and Gulmez Temur (Des ...
Some Artin-Schreier type function fields over finite fields with prescribed genus and number of rational places
ÇAKÇAK, Emrah; Özbudak, Ferruh (2007-07-01)
We give existence and characterization results for some Artin-Schreier type function fields over finite fields with prescribed genus and number of rational places simultaneously.
Bound-state solutions of the Klein-Gordon equation for the generalized PT-symmetric Hulthen potential
Egrifes, Harun; Sever, Ramazan (2007-04-01)
The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthen potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type.
Subfields of the function field of the deligne-Lusztig curve of ree type
Çakçak, Emrah; Akyıldız, Ersan; Özbudak, Ferruh; Department of Mathematics (2002)
Let X be the Deligne-Luzstig curve of Ree type defined over ¥q,q = 32s+1, s > 1 and F its function field. One of the main problem here is to construct a large number of nonrational subfields of F and compute their genera. For this, we consider the fixed fields FH, of F, under subgroups H of G, where G = Aut(F/F9) is the automor phism group of F/Fg. In this thesis, we show how one can compute the genera of FH for various subgroups H of G. Our computation here is based on the facts that: G is a Ree group whic...
Citation Formats
F. Özbudak, “Explicit maximal and minimal curves over finite fields of odd characteristics,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 81–92, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/33387.