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ON THE LEAST SQUAREFREE NUMBER IN AN ARITHMETIC PROGRESSION

Part of: Elementary number theory Multiplicative number theory

Published online by Cambridge University Press:  23 March 2017

R. M. Nunes
R. M. Nunes*
Affiliation:
EPFL SB MATHGEOM TAN, Station 8, CH-1015 Lausanne, Switzerland email ramon.moreiranunes@epfl.ch
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Abstract

We prove an asymptotic formula for squarefree numbers in arithmetic progressions, improving previous results by Prachar and Hooley. As a consequence we improve a lower bound of Heath-Brown for the least squarefree number in an arithmetic progression.

MSC classification

Primary: 11N37: Asymptotic results on arithmetic functions
Secondary: 11A07: Congruences; primitive roots; residue systems
Type
Research Article
Information
Mathematika , Volume 63 , Issue 2 , 2017 , pp. 483 - 498
Copyright
Copyright © University College London 2017 

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References

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