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math.AG2016
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…
math.AG2016
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…
math.NT2016
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…