Displaying similar documents to “The Erdős Theorem and the Halberstam Theorem in function fields”

Some Algebraic Properties of Polynomial Rings

Christoph Schwarzweller, Artur Korniłowicz (2016)

Formalized Mathematics

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In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.

Combinatorial Computations on an Extension of a Problem by Pál Turán

Gaydarov, Petar, Delchev, Konstantin (2015)

Serdica Journal of Computing

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Turan’s problem asks what is the maximal distance from a polynomial to the set of all irreducible polynomials over Z. It turns out it is sufficient to consider the problem in the setting of F2. Even though it is conjectured that there exists an absolute constant C such that the distance L(f - g) <= C, the problem remains open. Thus it attracts different approaches, one of which belongs to Lee, Ruskey and Williams, who study what the probability is for a set of polynomials ‘resembling’...

On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan

Simone Ugolini (2016)

Czechoslovak Mathematical Journal

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We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the Q -transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses,...

Mean value theorems for L-functions over prime polynomials for the rational function field

Julio C. Andrade, Jonathan P. Keating (2013)

Acta Arithmetica

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The first and second moments are established for the family of quadratic Dirichlet L-functions over the rational function field at the central point s=1/2, where the character χ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials P of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of P is large. The first moment obtained here is the function field analogue of a result due to...