One Hundred Years Uniform Distribution Modulo One and Recent Applications to Riemann’s Zeta-Function

Jörn Steuding ()
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Jörn Steuding: Würzburg University

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 659-698 from Springer

Abstract: Abstract We start with a brief account of the theory of uniform distribution modulo one founded by Weyl and others around 100 years ago (which is neither supposed to be complete nor historically depleting the topic). We present a few classical implications to diophantine approximation. However, our main focus is on applications to the Riemann zeta-function. Following Rademacher and Hlawka, we show that the ordinates of the nontrivial zeros of the zeta-function ζ(s) are uniformly distributed modulo one. We conclude with recent investigations concerning the distribution of the roots of the equation ζ(s) = a, where a is any complex number, and further questions about such uniformly distributed sequences.

Keywords: Riemann zeta-function; Zeros; a-points; Uniform distribution modulo one (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-06554-0_30

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DOI: 10.1007/978-3-319-06554-0_30

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