5 citations · 5 across the 6 of their papers we have counts for
9 papers
The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace
Yağmur Çakıroğlu, Oğuz Yayla, Emrah Sercan Yılmaz
We present the formula for the number of monic irreducible polynomials of degree over the finite field where the coefficients of and vanish for $n\g…
Number of Rational points of the Generalized Hermitian Curves over
Emrah Sercan Yılmaz
In this paper we consider the curves over and and find an exact formula for the number of -rational points o…
Explicit Maximal and Minimal Curves of Artin-Schreier Type from Quadratic Forms
Daniele Bartoli, Luciane Quoos, Zülfükar Saygı +1
In this work we present explicit examples of maximal and minimal curves over finite fields in odd characteristic. The curves are of Artin-Schreier type and the construction is clos…
Divisibility of L-Polynomials for a Family of Artin-Schreier Curves
Gary McGuire, Emrah Sercan Yılmaz
In this paper we consider the curves defined over and give a positive answer to a conjecture about a divisibility condition on -…
On the Zeta Functions of Supersingular Curves
Gary McGuire, Emrah Sercan Yılmaz
In general, the L-polynomial of a curve of genus is determined by coefficients. We show that the L-polynomial of a supersingular curve of genus is determined by fewer t…
Differential operators and hyperelliptic curves over finite fields
Iván Blanco-Chacón, Alberto F. Boix, Stiofáin Fordham +1
Boix, De Stefani and Vanzo have characterized ordinary/supersingular elliptic curves over in terms of the level of the defining cubic homogenous polynomial. We exten…
The Number of Irreducible Polynomials with the First Two Coefficients Fixed over Finite Fields of Odd Characteristic
Gary McGuire, Emrah Sercan Yılmaz
In this paper we give a different proof of Kuz'min's result on the number of irreducible polynomials with the first two coefficients fixed. Our technique is to relate the question…
Slope Estimates for Generalized Artin-Schreier Curves
Emrah Sercan Yılmaz, Gary McGuire
We provide first slope estimates of the Newton polygon of generalized Artin-Schreier curves, which are proved using the action of Frobenius and Verschiebung on cohomology. We provi…
Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients
Omran Ahmadi, Faruk Gologlu, Robert Granger +2
For any positive integers we present formulae for the number of irreducible polynomials of degree over the finite field where the coeffici…