The expression of a polynomial as a sum of three irreducibles

Hayes, David R.

doi:10.4064/aa-11-4-461-488

Cited by 58 publications

(39 citation statements)

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“…Any two fractions are pairwise separated by the norm of sizeQ −2 by ultrametric inequality (see (6)), and thus the arcs F (a/g,X) are pairwise disjoint. On the other hand, each term of S I is e(mα) with monic polynomial m, e(mα)e(−T X α) remains constant when α varies in norm of size < 1/X and thus |S I | is constant on F (α,X) for each α ∈ T. Thereforê…”

Section: Analysis On S Imentioning

confidence: 99%

Irreducible polynomials with several prescribed coefficients

2016

Finite Fields and Their Applications

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We study the number of irreducible polynomials over Fq with some coefficients prescribed. Using the technique developed by Bourgain, we show that there is an irreducible polynomial of degree n with r coefficients prescribed in any location when r ≤ [(1/4 − ǫ) n] for any ǫ > 0 and q is large; and when r ≤ δn for some δ > 0 and for any q. The result improves earlier work of Pollack stating that a similar result holds for r ≤ [(1 − ǫ)√ n].

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Section: Analysis On S Imentioning

confidence: 99%

Irreducible polynomials with several prescribed coefficients

2016

Finite Fields and Their Applications

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“…La proposition suivante rappelle un certain nombre de résultatsétablis dans [7] ou se démontrant de façon analogue. Nous n'en donnons pas la démonstration.…”

Section: I2 Le Caractère E Et La Mesure De Haarunclassified

Sums of cubes of polynomials

Car

Gallardo

2004

Acta Arith.

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“…Certaines analogies entre les propriétés arithmétiques de l'anneau F q [X] et l'anneau Z des entiers relatifs ontété mises enévidence. En particulier, en ce qui concerne l'arithmétique additive, les problèmes de Waring [18] et de Goldbach [14] ontétéétudiés et plus particulièrement le problème de Waring pour les carrés ( [6]- [12]). …”

Section: Une Généralisation Du Problème De Waring-goldbach Polynomialunclassified

“…Nous rappelons ici quelques résultatsétablis dans [14] que nous utiliserons fréquemment par la suite. …”

Section: Notations Et Conventionsunclassified