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THE INTERSECTION OF PIATETSKI-SHAPIRO SEQUENCES

Part of: Exponential sums and character sums

Published online by Cambridge University Press:  01 April 2014

Roger C. Baker
Roger C. Baker*
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602,U.S.A. email baker@math.byu.edu
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Abstract

We give an asymptotic formula for the number of primes $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p \le x$ of the form $p = [n_1^{c_1}] = \cdots = [n_d^{c_d}]$, where $c_1, \ldots, c_d$ are greater than 1 but “sufficiently close” to 1. This improves work of E. R. Sirota $(d=2)$ and W. Zhai $(d \ge 3)$.

MSC classification

Secondary: 11L20: Sums over primes
Type
Research Article
Information
Mathematika , Volume 60 , Issue 2 , July 2014 , pp. 347 - 362
Copyright
Copyright © University College London 2014 

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