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

Published online by Cambridge University Press:  20 November 2018

M. Z. Garaev
M. Z. Garaev*
Affiliation:
Instituto de Matemáticas, Universidad Nacional Áutonoma de México, Campus Morelia, Ap. Postal 61-3 (Xangari), C.P. 58089, Morelia, Michoacán, México, garaev@matmor.unam.mx
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Abstract

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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 $p$ .

Keywords

11L0711N36Large sieveexponential sums

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 2 , 01 April 2009 , pp. 336 - 350
Copyright
Copyright © Canadian Mathematical Society 2009

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