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IMPROVING AN INEQUALITY FOR THE DIVISOR FUNCTION

Part of: Multiplicative number theory

Published online by Cambridge University Press:  28 March 2018

JEFFREY P. S. LAY Open the ORCID record for JEFFREY P. S. LAY [Opens in a new window]
JEFFREY P. S. LAY*
Affiliation:
Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia email jeffrey.lay@anu.edu.au
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Abstract

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Using elementary means, we improve an explicit bound on the divisor function due to Friedlander and Iwaniec [Opera de Cribro, American Mathematical Society, Providence, RI, 2010]. Consequently, we modestly improve a result regarding a sieving inequality for Gaussian sequences.

Keywords

divisor functionsmall divisorsGaussian sequencessieve estimates

MSC classification

Primary: 11N56: Rate of growth of arithmetic functions
Secondary: 11N36: Applications of sieve methods 11N37: Asymptotic results on arithmetic functions 11N64: Other results on the distribution of values or the characterization of arithmetic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 3 , June 2018 , pp. 374 - 381
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Friedlander, J. and Iwaniec, H., ‘Gaussian sequences in arithmetic progressions’, Funct. Approx. Comment. Math. 37(1) (2007), 149–157.CrossRefGoogle Scholar
Friedlander, J. and Iwaniec, H., Opera de Cribro (American Mathematical Society, Providence, RI, 2010).CrossRefGoogle Scholar
Iwaniec, H. and Munshi, R., ‘Cubic polynomials and quadratic forms’, J. Lond. Math. Soc. (2) 81(1) (2010), 45–64.CrossRefGoogle Scholar
Landreau, B., ‘Majorations de fonctions arithmétiques en moyenne sur des ensembles de faible densité’, Sémin. Théor. Nombres 1987–1988 (1988), 18 pages.Google Scholar