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Plus grand facteur premier de valeurs de polynômes aux entiers

100%

de la Bretèche R.

Acta Arithmetica

2015

tom 169

nr 3

221-250

Let P⁺(n) denote the largest prime factor of the integer n. Using the Heath-Brown and Dartyge methods, we prove that for any even unitary irreducible quartic polynomial Φ with integral coefficients and the associated Galois group isomorphic to V₄, there exists a positive constant $c_Φ$ such that the set of integers n ≤ X satisfying $P⁺(Φ(n)) ≥ X^{1+c_Φ}$ has a positive density. Such a result was recently proved by Dartyge for Φ(n) = n⁴ - n² + 1. There is an appendix written with Jean-François Mestre.

Sommes sans grand facteur premier

100%

de la Bretèche R.

Acta Arithmetica

1999

tom 88

nr 1

1-14

Sums of arithmetic functions over values of binary forms

63%

de la Bretèche R., Browning T.

Acta Arithmetica

2006

tom 125

nr 3

291-304

Ograniczanie wyników

3 Acta Arithmetica

3 de la Bretèche R.

1 Browning T.

1 2015

1 2006

1 1999

Wyniki wyszukiwania

Plus grand facteur premier de valeurs de polynômes aux entiers

Sommes sans grand facteur premier

Sums of arithmetic functions over values of binary forms