<abstract xmlns="http://www.w3.org/1999/xhtml">For a function <italic>f</italic> satisfying <italic>f</italic> (<italic>x</italic>) = <italic>o</italic>((log <italic>x</italic>) <italic>K</italic>), <italic>K ></italic> 0, and a sequence of numbers (<italic>qn</italic>) <italic>n</italic>, we prove by assuming several conditions on <italic>f</italic> that the sequence (<italic>αf</italic> (<italic>qn</italic>)) <italic>n≥n</italic>0 is uniformly distributed modulo one for any nonzero real number <italic>α</italic>. This generalises some former results due to Too, Goto and Kano where instead of (<italic>qn</italic>) <italic>n</italic> the sequence of primes was considered.</abstract>

For a function f satisfying f (x) = o((log x) K), K > 0, and a sequence of numbers (qn) n, we prove by assuming several conditions on f that the sequence (αf (qn)) n≥n0 is uniformly distributed modulo one for any nonzero real number α. This generalises some former results due to Too, Goto and Kano where instead of (qn) n the sequence of primes was considered.

Log-Like Functions and Uniform Distribution Modulo One

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Log-Like Functions and Uniform Distribution Modulo One"}

For a function f satisfying f (x) = o((log x) K), K > 0, and a sequence of numbers (qn) n, we prove by assuming several conditions on f that the sequence (αf...

Log-Like Functions and Uniform Distribution Modulo One

Published Online: Jan 25, 2019

Page range: 93 - 101

Received: Oct 20, 2017

Accepted: Feb 02, 2018

DOI: https://doi.org/10.2478/udt-2018-0013

Keywords
Uniform Distribution, Discrepancy

© 2018 Martin Rehberg, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Log-Like Functions and Uniform Distribution Modulo One

Published Online: Jan 25, 2019

Page range: 93 - 101

Received: Oct 20, 2017

Accepted: Feb 02, 2018

DOI: https://doi.org/10.2478/udt-2018-0013

KeywordsUniform Distribution, Discrepancy

© 2018 Martin Rehberg, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Uniform Distribution, Discrepancy