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Prime numbers of the form [nc]

Published online by Cambridge University Press:  25 July 2002

J. Rivat  and
J. Wu
J. Rivat
Affiliation:
Institut Elie Cartan, UMR 7502 UHP-CNRS-INRIA, Université Henri Poincaré (Nancy 1), 54506 Vandœuvre-lès-Nancy, France. e-mail: rivat@iecn.u-nancy.fr, wujie@iecn.u-nancy.fr
J. Wu
Affiliation:
Institut Elie Cartan, UMR 7502 UHP-CNRS-INRIA, Université Henri Poincaré (Nancy 1), 54506 Vandœuvre-lès-Nancy, France. e-mail: rivat@iecn.u-nancy.fr, wujie@iecn.u-nancy.fr
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Abstract

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In 1953, Pjateckii˘-S˘apiro has proved that there are infinitely many primes of the form [n^c] for 1 [less than] c [less than] {12\over11} (with an asymptotic result). This range, which measures our progress in the technique of exponential sums, has been improved by many authors. In this paper we obtain 1 [less than] c\leq{243\over205}.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 2 , May 2001 , pp. 237 - 254
Copyright
2001 Glasgow Mathematical Journal Trust