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A LOWER BOUND FOR THE LARGE SIEVE WITH SQUARE MODULI

Part of: Diophantine approximation, transcendental number theory Exponential sums and character sums Sequences and sets Multiplicative 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 [email protected]
SEAN B. LYNCH*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, UNSW-Sydney, NSW 2052, Australia email [email protected]
LIANGYI ZHAO
Affiliation:
School of Mathematics and Statistics, University of New South Wales, UNSW-Sydney, NSW 2052, Australia email [email protected]
*
✉[email protected]
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Abstract

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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. 

Footnotes

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

References

Baier, S. and Zhao, L., ‘Bombieri–Vinogradov theorem for sparse sets of moduli’, Acta Arith. 125(2) (2006), 187–201.10.4064/aa125-2-5Google Scholar
Baier, S. and Zhao, L., ‘An improvement for the large sieve for square moduli’, J. Number Theory 128(1) (2008), 154–174.Google Scholar
Banks, W. D., Pappalardi, F. and Shparlinski, I. E., ‘On group structures realized by elliptic curves over arbitrary finite fields’, Exp. Math. 21(1) (2012), 11–25.10.1080/10586458.2011.606075Google Scholar
Bourgain, J., Ford, K., Konyagin, S. V. and Shparlinski, I. E., ‘On the divisibility of Fermat quotients’, Michigan Math. J. 59 (2010), 313–328.10.1307/mmj/1281531459Google Scholar
Halupczok, K., ‘A new bound for the large sieve inequality with power moduli’, Int. J. Number Theory 8(3) (2012), 689–695.Google Scholar
Matomäki, K., ‘A note on primes of the form p = aq 2 + 1’, Acta Arith. 137 (2009), 133–137.Google Scholar
Shparlinski, I. E. and Zhao, L., ‘Elliptic curves in isogeny classes’, J. Number Theory 191 (2018), 194–212.Google Scholar
Zhao, L., ‘Large sieve inequality for characters to square moduli’, Acta Arith. 112(3) (2004), 297–308.Google Scholar