The large sieve for $2^{[O(n^{15/14+o(1)})]}$ modulo primes

M. Z. Garaev

The large sieve for $2^{[O(n^{15/14+o(1)})]}$ modulo primes

Number Theory 2007-05-23 v2

Authors: M. Z. Garaev

Abstract

Let $\lambda$ be a fixed integer, $\lambda\ge 2.$ Let $s_n$ be any strictly increasing sequence of positive integers satisfying $s_n\le n^{15/14+o(1)}.$ In this paper we give a version of the large sieve inequality for the sequence $\lambda^{s_n}.$ In particular, we prove that for $\pi(X)(1+o(1))$ primes $p, \ p\le X,$ the numbers $\lambda^{s_n},\quad n\le X(\log X)^{2+\epsilon}$ are uniformly distributed modulo $p.$

Keywords

prime number theory prime numbers multiplicative functions

Cite

@article{arxiv.math/0505396,
  title  = {The large sieve for $2^{[O(n^{15/14+o(1)})]}$ modulo primes},
  author = {M. Z. Garaev},
  journal= {arXiv preprint arXiv:math/0505396},
  year   = {2007}
}

Comments

19 pages; in the new version we clean up some estimates and add several more consequences of the main result

The large sieve for $2^{[O(n^{15/14+o(1)})]}$ modulo primes

Abstract

Keywords

Cite

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