<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We give two applications of uniform distribution theory to the Riemann zeta-function. We show that the values of the argument of <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-10.jpg"></inline-graphic></alternatives></inline-formula> are uniformly distributed modulo <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-11.jpg"></inline-graphic></alternatives></inline-formula>, where P(n) denotes the values of a polynomial with real coefficients evaluated at the positive integers. Moreover, we study the distribution of arg <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-12.jpg"></inline-graphic></alternatives></inline-formula> modulo π, where γ<sub>n</sub> is the nth ordinate of a zeta zero in the upper half-plane (in ascending order). </p></abstract>

We give two applications of uniform distribution theory to the Riemann zeta-function. We show that the values of the argument of  are uniformly distributed modulo , where P(n) denotes the values of a polynomial with real coefficients evaluated at the positive integers. Moreover, we study the distribution of arg  modulo π, where γn is the nth ordinate of a zeta zero in the upper half-plane (in ascending order).

Applications of uniform distribution theory to the Riemann zeta-function

Akdeniz University Department of Mathematics TR–07-058 Antalya TURKEY

Department of Mathematics Würzburg University Emil-Fischer-Str. 40 D–97-074 Würzburg GERMANY

Tatra Mountains Mathematical Publications

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

{"article-title":"Applications of uniform distribution theory to the Riemann zeta-function"}

We give two applications of uniform distribution theory to the Riemann zeta-function. We show that the values of the argument of  are uniformly distributed...

Applications of uniform distribution theory to the Riemann zeta-function

Published Online: Feb 19, 2016

Page range: 67 - 74

Received: Oct 21, 2015

DOI: https://doi.org/10.1515/tmmp-2015-0042

Keywords
Riemann zeta-function, uniform distribution

© 2016

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

Applications of uniform distribution theory to the Riemann zeta-function

Published Online: Feb 19, 2016

Page range: 67 - 74

Received: Oct 21, 2015

DOI: https://doi.org/10.1515/tmmp-2015-0042

KeywordsRiemann zeta-function, uniform distribution

© 2016

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

Keywords
Riemann zeta-function, uniform distribution