On the distribution in the arithmetic progressions of reducible quadratic polynomials in short intervals, II
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Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 1, pp. 93-102.

This paper gives further results about the distribution in the arithmetic progressions (modulo a product of two primes) of reducible quadratic polynomials (an+b)(cn+d) in short intervals n[x,x+x ϑ ], where now ϑ(0,1]. Here we use the Dispersion Method instead of the Large Sieve to get results beyond the classical level ϑ, reaching 3ϑ/2 (thus improving also the level of the previous paper, i.e. 3ϑ-3/2), but our new results are different in structure. Then, we make a graphical comparison of the two methods.

Ce texte donne de nouveaux résultats sur la répartition dans les progressions arithmétiques (modulo un produit de deux nombres premiers) des valeurs (an+b)(cn+d) prises par un polynôme quadratique réductible lorsque l’entier n varie dans des intervalles courts n[x,x+x ϑ ], où ϑ(0,1]. Nous utilisons ici la méthode de dispersion, pour obtenir un niveau de répartition au delà du niveau classique θ. Nous obtenons pour niveau 3ϑ/2, améliorant en cela la valeur 3ϑ-3/2 obtenue par le grand crible. Nous terminons par une comparaison graphique des deux approches.

@article{JTNB_2001__13_1_93_0,
     author = {Coppola, Giovanni and Salerno, Saverio},
     title = {On the distribution in the arithmetic progressions of reducible quadratic polynomials in short intervals, II},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {13},
     number = {1},
     year = {2001},
     pages = {93-102},
     zbl = {1046.11068},
     mrnumber = {1838072},
     language = {en},
     url={jtnb.centre-mersenne.org/item/JTNB_2001__13_1_93_0/}
}
Coppola, Giovanni; Salerno, Saverio. On the distribution in the arithmetic progressions of reducible quadratic polynomials in short intervals, II. Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 1, pp. 93-102. https://jtnb.centre-mersenne.org/item/JTNB_2001__13_1_93_0/

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