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

M. Z. Garaev
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Abstract

Let $λ$ be a fixed integer, $λ\ge 2.$ 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 $λ^{s_n}.$ In particular, we prove that for $π(X)(1+o(1))$ primes $p, \ p\le X,$ the numbers $$ λ^{s_n},\quad n\le X(\log X)^{2+ε} $$ are uniformly distributed modulo $p.$

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M. Z. Garaev. 2005-09-01. The large sieve for $2^{[O(n^{15/14+o(1)})]}$ modulo primes. https://arxiv.org/abs/math/0505396

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