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On the Uniform Distribution of Some Sequences
Author(s) -
Leitmann Dieter
Publication year - 1976
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-14.3.430
Subject(s) - sequence (biology) , combinatorics , integer (computer science) , prime (order theory) , mathematics , distribution (mathematics) , mod , uniform distribution (continuous) , prime number , discrete mathematics , computer science , mathematical analysis , statistics , biology , genetics , programming language
In this paper it is shown that the sequence { p γ } ( p runs through the prime numbers) is uniformly distributed mod 1, if γ is greater than one and not an integer. The method used here is a modification of that of Pjateckij‐Shapiro in [ 1 ], to estimate the sum Σ N < P ⩽2 N e{kp γ ).