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A LOWER BOUND FOR THE LARGE SIEVE WITH SQUARE MODULI

Part of: Sequences and sets Multiplicative number theory Exponential sums and character sums Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  27 February 2019

STEPHAN BAIER Open the ORCID record for STEPHAN BAIER [Opens in a new window] ,
SEAN B. LYNCH Open the ORCID record for SEAN B. LYNCH [Opens in a new window]  and
LIANGYI ZHAO Open the ORCID record for LIANGYI ZHAO [Opens in a new window]
STEPHAN BAIER
Affiliation:
Department of Mathematics, RKMVERI, G.T. Road, Belur Math, Howrah, West Bengal 711202, India email stephanbaier2017@gmail.com
SEAN B. LYNCH*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, UNSW-Sydney, NSW 2052, Australia email s.b.lynch@unsw.edu.au
LIANGYI ZHAO
Affiliation:
School of Mathematics and Statistics, University of New South Wales, UNSW-Sydney, NSW 2052, Australia email l.zhao@unsw.edu.au
*
✉s.b.lynch@unsw.edu.au
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Abstract

We prove a lower bound for the large sieve with square moduli.

Keywords

large sieveFarey fractions in short intervalsestimates on exponential sums

MSC classification

Primary: 11N35: Sieves
Secondary: 11B57: Farey sequences; the sequences ${1^k, 2^k, cdots}$ 11J25: Diophantine inequalities 11J71: Distribution modulo one 11L03: Trigonometric and exponential sums, general 11L07: Estimates on exponential sums 11L40: Estimates on character sums
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 2 , October 2019 , pp. 225 - 229
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

The third author was supported by the FRG grant PS43707 and the Faculty Silverstar Fund PS49334 at UNSW during this work.

References

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