On the exponential large sieve inequality for sparse sequences modulo primes

Abstract

We complement the argument of M. Z. Garaev (2009) with several other ideas to obtain a stronger version of the large sieve inequality with sparse exponential sequences of the form ${\lambda }^{s_n}$. In particular, we obtain a result which is non-trivial for monotonically increasing sequences $\mathcal{S}=\{s_n{\}}_{n=1}^{\infty }$ provided $s_n\le n^{2+o(1)}$, whereas the original argument of M. Z. Garaev requires $s_n\le n^{15/14+o(1)}$ in the same setting. We also give an application of our result to arithmetic properties of integers with almost all digits prescribed.

Version 2, with Mei-Chu Chang as a co-author, extends the range in which Version 1 worked

References in corpus (1)

• Some new inequalities in additive combinatorics