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POWER-FREE VALUES OF THE POLYNOMIAL t1⋯tr−1

Part of: Multiplicative number theory

Published online by Cambridge University Press:  23 September 2011

PIERRE LE BOUDEC
PIERRE LE BOUDEC*
Affiliation:
Université Denis Diderot (Paris VII), Institut de Mathématiques de Jussieu, UMR 7586, Case 7012 - Bâtiment Chevaleret, Bureau 7C14, 75205 Paris Cedex 13, France (email: pleboude@math.jussieu.fr)
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Abstract

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Let k,r≥2 be two integers. We prove an asymptotic formula for the number of k-free values of the r variables polynomial t1⋯tr−1 over [1,x]r∩ℤr.

Keywords

power-free values of polynomialsequidistribution in arithmetic progressionsKloosterman sums

MSC classification

Secondary: 11N32: Primes represented by polynomials; other multiplicative structure of polynomial values
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 154 - 163
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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