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2017 | OriginalPaper | Chapter

Local Oscillations in Moderately Dense Sequences of Primes

Authors : Jörg Brüdern, Christian Elsholtz

Published in: Number Theory – Diophantine Problems, Uniform Distribution and Applications

Publisher: Springer International Publishing

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Abstract

The distribution of differences of consecutive members of sequences of primes is investigated. A quantitative measure for oscillations among these differences is the curvature of the sequence. If the sequence is not too sparse, then sharp estimates for its curvature are provided.

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previous chapter Diversity in Parametric Families of Number Fields

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It may seem unnatural to include the lower bound on δ in this definition, but more rapidly decaying functions will play no role in this paper, and it simplifies the exposition later that δ is not too small, a fortiori.

P. Erdős, A. Rényi, Some problems and results on consecutive primes. Simon Stevin 27, 115–125 (1950)MathSciNetMATH

P. Erdős, P. Turán, On some new questions on the distribution of prime numbers. Bull. Am. Math. Soc. 54, 371–378 (1948)MathSciNetCrossRefMATH

P.X. Gallagher, On the distribution of primes in short intervals. Mathematika 23, 4–9 (1976)MathSciNetCrossRefMATH

H. Halberstam, H.-E. Richert, Sieve Methods. London Mathematical Society Monographs, vol. 4 (Academic, London/New York, 1974)

G.H. Hardy, J.E. Littlewood, Some problems of “Partitio Numerorum”: III. On the expression of a number as a sum of primes. Acta Math. 44, 1–70 (1922)MATH

C. Pomerance, The prime number graph. Math. Comp. 33, 399–408 (1979)MathSciNetCrossRefMATH

K. Prachar, Bemerkung zu einer Arbeit von Erdős und Rényi und Berichtigung. Monatsh. Math. 58, 117 (1954)MathSciNetCrossRefMATH

A. Rényi, On a theorem of Erdős and Turán. Proc. Am. Math. Soc. 1, 7–10 (1950)MATH

Title: Local Oscillations in Moderately Dense Sequences of Primes
Authors: Jörg Brüdern
Christian Elsholtz
Publisher: Springer International Publishing
Book: Number Theory – Diophantine Problems, Uniform Distribution and Applications
Print ISBN: 978-3-319-55356-6

Electronic ISBN: 978-3-319-55357-3

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-55357-3_8

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