Type: Article

The large sieve inequality for the exponential sequence lambda^[O(n^15/14+o(1))] modulo primes

M. Z. Garaev;

Abstract:

Let lambda be a fixed integer exceeding l and s(n) any strictly increasing sequence of positive integers satisfying s(n) <= n(15/14-o(1)). In this paper we give a version of the large sieve inequality for the sequence lambda(5n). In particular, we obtain nontrivial estimates of the associated trigonometric sums "on average" and establish equidistribution properties of the numbers lambda(5n), n <= p(log p)(2), modulo p for most primers p.