On the distribution in the arithmetic progressions of reducible quadratic polynomials

S. Salerno, A. Vitolo

University of Salerno

Abstract: 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.

UDC: 511

MSC: 11B25

Received: 20.01.1994

Language: English

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1995, 45:1, 215–228

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