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A Divisor Problem for Values of Polynomials

Published online by Cambridge University Press:  20 November 2018

Armel Mercier  and
Werner Georg Nowak
Armel Mercier
Affiliation:
Département de mathématiques Université du Québec à Chicoutimi 555 boul. Université Chicoutimi, Prov. de Québec G7H2B1, Canada
Werner Georg Nowak
Affiliation:
Institut für Mathematik der Universitât fur Bodenkultur Greg or Mendel-Strafie 33 A-1180 Wien, Austria
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Abstract

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In this article we investigate the average order of the arithmetical function

where p1(t), p2(t) are polynomials in Z [t], of equal degree, positive and increasing for t ≥ 1. Using the modern method for the estimation of exponential sums ("Discrete Hardy-Littlewood Method"), we establish an asymptotic result which is as sharp as the best one known for the classical divisor problem.

Résumé

Résumé

Dans cet article, on étudie l'ordre moyen de la fonction arithmétique

où p1(t),p2(t) sont des polynômes dans Z[t], de degrés égaux, qui sont positifs et croissants pour t ≥ 1. En utilisant la méthode moderne pour l'estimation de sommes exponentielles ("méthode discrète de Hardy-Littlewood"), on obtient un comportement asymptotique, aussi précis que le meilleur résultat connu, concernant le problème classique des diviseurs.

Keywords

10H2510G1010J25.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 108 - 115
Copyright
Copyright © Canadian Mathematical Society 1992

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