An extension of the Piatetski-Shapiro prime number theorem

Baier, Stephan (2005) An extension of the Piatetski-Shapiro prime number theorem. Analysis (Munich), 25 (1). pp. 87-98.

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Abstract

Balog and Harman proved that for any λ in the interval 1/2 ≤ λ < 1 and any real θ there are infinitely many primes p satisfying (with an asymptotic result). In the present paper we prove that for 59/85 = 0-694... < λ < 1 the above expo­nent -(1-λ)/2+ε may be replaced by - min{max{(35-22λ)/129, 1/7}, 5/18-λ/6}+ε. This result in particular contains the Piatetski-Shapiro prime number theorem in the ver­sion given by Liu and Rivat: We have |{n ≤ N : [nc] prime}) ~ N/(c log N) as N → 8734 if 1 < c < 15/13. For the proof of our result we use exponential sum techniques.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Number Theory, Ergodic Theory and Dynamical Systems (former - to 2013) Faculty of Science > Research Groups > Number Theory (former - to 2017)
Depositing User:	Pure Connector
Date Deposited:	07 Sep 2013 05:12
Last Modified:	24 Jun 2024 11:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/43197
DOI:	10.1515/anly-2005-0106

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