Geodesic
On~the~distribution in the~arithmetic progressions of reducible quadratic polynomials
Izvestiya. Mathematics , Tome 45 (1995) no. 1, pp. 215-228.

Voir la notice de l'article provenant de la source Math-Net.Ru

By using Weil's estimate for Kloosterman sums, we obtain a result about the distribution of the sequence $n(n+2)$, beyond the classical level, when a bilinear form with support over pairs of prime moduli is considered. We also obtain an analogous result in the case of a trilinear form, but only by using the recent results for sums of Kloosterman sums of Deshouillers–Iwaniec. Furthermore the method is extended to consider general quadratic reducible polynomials. 
@article{IM2_1995_45_1_a11,
     author = {S. Salerno and A. Vitolo},
     title = {On~the~distribution in the~arithmetic progressions of reducible quadratic polynomials},
     journal = {Izvestiya. Mathematics },
     pages = {215--228},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_45_1_a11/}
}
TY  - JOUR
AU  - S. Salerno
AU  - A. Vitolo
TI  - On~the~distribution in the~arithmetic progressions of reducible quadratic polynomials
JO  - Izvestiya. Mathematics 
PY  - 1995
SP  - 215
EP  - 228
VL  - 45
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1995_45_1_a11/
LA  - en
ID  - IM2_1995_45_1_a11
ER  - 
%0 Journal Article
%A S. Salerno
%A A. Vitolo
%T On~the~distribution in the~arithmetic progressions of reducible quadratic polynomials
%J Izvestiya. Mathematics 
%D 1995
%P 215-228
%V 45
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1995_45_1_a11/
%G en
%F IM2_1995_45_1_a11
S. Salerno; A. Vitolo. On~the~distribution in the~arithmetic progressions of reducible quadratic polynomials. Izvestiya. Mathematics , Tome 45 (1995) no. 1, pp. 215-228. http://geodesic.mathdoc.fr/item/IM2_1995_45_1_a11/

[1] E. Bombieri, J. B. Friedlander, H. Iwaniec, “Primes in arithmetic progressions to large moduli”, Acta Math., 156 (1986), 203–251 | DOI | MR | Zbl

[2] J. M. Deshouillers, H. Iwaniec, “Kloosterman sums and Fourier coefficients of cusp forms”, Inv. Math., 70 (1986), 203–251 | MR

[3] J. B. Friedlander, H. Iwaniec, “Quadratic polynomials and quadratic forms”, Acta Math., 141 (1978) | DOI | MR | Zbl

[4] H. Halberstam, H. E. Richert, Sieve Methods, Acad. Press, London, 1974 | MR | Zbl

[5] C. Hooley, “On the problem of divisors of quadratic polynomials”, Acta Math., 110 (1963), 97–114 | DOI | MR | Zbl

[6] C. Hooley, “On the greatest prime factor of a quadratic polynomial”, Acta Math., 117 (1967), 281–299 | DOI | MR | Zbl

[7] H. Iwaniec, “Almost-primes represented by quadratic polynomials”, Inv. Math., 47 (1978), 171–188 | DOI | MR | Zbl