The Large Sieve Inequality for the Exponential Sequence λ[O(n15/14+o(1))] Modulo Primes

Garaev, M. Z.

Canadian journal of mathematics, Tome 61 (2009) no. 2, pp. 336-350

Résumé

Let $\lambda $ be a fixed integer exceeding 1 and ${{s}_{n}}$ 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 obtain nontrivial estimates of the associated trigonometric sums “on average” and establish equidistribution properties of the numbers ${{\lambda }^{{{s}_{n}}}},n\le p{{(\log p)}^{2+\varepsilon }}$ , modulo $p$ for most primes $p$ .

Détail

DOI : 10.4153/CJM-2009-017-3

Mots-clés : 11L07, 11N36, Large sieve, exponential sums

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