On the number of zero trace elements in polynomial bases for F2n.

Igor E. Shparlinski

Displaying similar documents to “On the number of zero trace elements in polynomial bases for F2n.”

Canonical bases for subalgebras on two generators in the univariate polynomial ring.

Torstensson, Anna (2002)

Beiträge zur Algebra und Geometrie

Similarity:

Lehmer’s conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves

Joseph H. Silverman (2012)

Journal de Théorie des Nombres de Bordeaux

Similarity:

A number of authors have proven explicit versions of Lehmer’s conjecture for polynomials whose coefficients are all congruent to $1$ modulo $m$ . We prove a similar result for polynomials $f (X)$ that are divisible in $(ℤ / m ℤ) [X]$ by a polynomial of the form $1 + X + \dots + X^{n}$ for some $n \geq ϵ deg (f)$ . We also formulate and prove an analogous statement for elliptic curves.

On a limit point associated with the abc-conjecture

Michael Filaseta, Sergeĭ Konyagin (1998)

Colloquium Mathematicae

Similarity:

Factoring polynomials over global fields

Karim Belabas, Mark van Hoeij, Jürgen Klüners, Allan Steel (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We prove that van Hoeij’s original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well as natural variants. In particular, our approach also yields polynomial time complexity results for bivariate polynomials over a finite field.

Complete polynomial vector fields in a ball.

Ben Yousif, N.M. (2004)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Similarity:

Identities arising from higher-order Daehee polynomial bases

Dae San Kim, Taekyun Kim (2015)

Open Mathematics

Similarity:

Here we will derive formulas for expressing any polynomial as linear combinations of two kinds of higherorder Daehee polynomial basis. Then we will apply these formulas to certain polynomials in order to get new and interesting identities involving higher-order Daehee polynomials of the first kind and of the second kind.

Power-free values, large deviations, and integer points on irrational curves

Harald A. Helfgott (2007)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $f \in ℤ [x]$ be a polynomial of degree $d \geq 3$ without roots of multiplicity $d$ or $(d - 1)$ . Erdős conjectured that, if $f$ satisfies the necessary local conditions, then $f (p)$ is free of $(d - 1)$ th powers for infinitely many primes $p$ . This is proved here for all $f$ with sufficiently high entropy. The proof serves to demonstrate two innovations: a strong repulsion principle for integer points on curves of positive genus, and a number-theoretical analogue of Sanov’s theorem from the theory of large deviations. ...