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.

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.

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Giovanni Coppola; Saverio Salerno. 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. doi : 10.5802/jtnb.306. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.306/

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