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A LOWER BOUND FOR THE LARGE SIEVE WITH SQUARE MODULI

  • STEPHAN BAIER (a1), SEAN B. LYNCH (a2) and LIANGYI ZHAO (a3)

Abstract

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

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

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References

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[1] Baier, S. and Zhao, L., ‘Bombieri–Vinogradov theorem for sparse sets of moduli’, Acta Arith. 125(2) (2006), 187201.10.4064/aa125-2-5
[2] Baier, S. and Zhao, L., ‘An improvement for the large sieve for square moduli’, J. Number Theory 128(1) (2008), 154174.
[3] 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), 1125.10.1080/10586458.2011.606075
[4] Bourgain, J., Ford, K., Konyagin, S. V. and Shparlinski, I. E., ‘On the divisibility of Fermat quotients’, Michigan Math. J. 59 (2010), 313328.10.1307/mmj/1281531459
[5] Halupczok, K., ‘A new bound for the large sieve inequality with power moduli’, Int. J. Number Theory 8(3) (2012), 689695.
[6] Matomäki, K., ‘A note on primes of the form p = aq 2 + 1’, Acta Arith. 137 (2009), 133137.
[7] Shparlinski, I. E. and Zhao, L., ‘Elliptic curves in isogeny classes’, J. Number Theory 191 (2018), 194212.
[8] Zhao, L., ‘Large sieve inequality for characters to square moduli’, Acta Arith. 112(3) (2004), 297308.
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A LOWER BOUND FOR THE LARGE SIEVE WITH SQUARE MODULI

  • STEPHAN BAIER (a1), SEAN B. LYNCH (a2) and LIANGYI ZHAO (a3)

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