Nombres premiers de la forme ⌊nc⌋

2001/04/01 by Joël Rivat, Patrick Sargos · 10 citations
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Algebraic Geometry and Number Theory

paper · pdf · doi:10.4153/cjm-2001-017-0

Abstract

Abstract For c > 1 we denote by πc(x) the number of integers n ≤ x such that ⌊n c ⌋ is prime. In 1953, Piatetski-Shapiro has proved that holds for c < 12/11. Many authors have extended this range, which measures our progress in exponential sums techniques. In this article we obtain c < 1.16117….

Citations

• Prime Numbers in Short Intervals and a Generalized Vaughan Identity

Cited by

• Roth-type theorem for quadratic system in Piatetski-Shapiro primes
• A Remark on the Piatetski-Shapiro-Hua Theorem
• An Additive Problem over Piatetski-Shapiro Primes and Almost-primes
• How often are \lfloor n^α \rfloor and \lfloor n^β \rfloor simultaneously primes?
• Diophantine approximation with mixed powers of Piatetski-Shapiro primes
• Vinogradov's three primes theorem in the intersection of multiple Piatetski-Shapiro sets
• Cubic Waring-Goldbach problem with Piatetski-Shapiro primes
• Some arithmetic properties of numbers of the form \lfloor p^c\rfloor
• Exponential sums with polynomials and their applications to primes in sparse sets
• Prime numbers of the form [n^c tan^θ(log n)]

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