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

2005/05/18 by M. Z. Garaev, Garaev, M. Z.
Mathematics · #11L07 #11N36 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11L07 #msc:11N36

paper · pdf · doi:10.48550/arxiv.math/0505396

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

arxiv created 2005/09/01 · arxiv updated 2009/12/01

Abstract

Let λ be a fixed integer, λ≥ 2. Let s_n be 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 λ^s_n. In particular, we prove that for π(X)(1+o(1)) primes p, p≤ X, the numbers λ^s_n, n≤ X(log X)^2+ε are uniformly distributed modulo p.

Related

• On the exponential large sieve inequality for sparse sequences modulo primes
• Large sieve with sparse sets of moduli for ℤ[i]
• On the large sieve with sparse sets of moduli
• Polynomial values modulo primes on average and sharpness of the larger sieve
• On a variant of the large sieve