On the exponential large sieve inequality for sparse sequences modulo primes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Chang, Mei-Chu¹  Kerr, Bryce²  Shparlinski, Igor E.² 

[1] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

[2] Univ New South Wales, Dept Pure Math, Sydney, NSW 2052, Australia

关键词: Exponential sums;    Sparse sequences;    Large sieve;   

DOI  :  10.1016/j.jmaa.2017.10.070

来源: Elsevier

【 摘 要 】

We complement the argument of M. Z. Garaev (2009) [9] with several other ideas to obtain a stronger version of the large sieve inequality with sparse exponential sequences of the form lambda(s pi) . In particular, we obtain a result which is non-trivial for monotonically increasing sequences S = {s(n)}(n=1)(infinity) provided s(n) <= N2+o(1), whereas the original argument of M. Z. Garaev requires s(n) <= n(15/14+o(1)) in the same setting. We also give an application of our result to arithmetic properties of integers with almost all digits prescribed. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free