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

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

2005-05-18

arxiv.org/abs/math/0505396v2

Mathematics

Number Theory

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

Scientific paper

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 $p.$

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