# Jan Büthe

## Office

Endenicher Allee 60, room 1.025
Phone: +49 (0) 228 73-62270
E-mail: jbuethe(at)math.uni-bonn.de

## Research Interests

I am a postdoc interested in number theory. In my thesis , which I wrote under supervision of Prof. Dr. Jens Franke, I have been concerned with questions related to partial numerical verifications of the Riemann hypothesis. I am currently interested in the analytic theory of L-functions.

## Publications

• (with J. Franke, T. Kleinjung and A. Jost) Some applications of the Weil-Barner explicit formula. 2013, Math. Nachr., 286: 536-549.
• A method for proving the completeness of a list of zeros of certain L-functions, 2013, Math. Comp., 84: 2413-2431. preprint version: arXiv:1308.6704
• A Brun-Titchmarsh Inequality for weighted sums over prime numbers, 2014, Acta Arith., 166(3): 289-299. preprint version: arXiv:1410.7561
• (with J. Franke, T. Kleinjung and A. Jost) A practical analytic method for calculating $\pi(x)$ . accepted for publication in Math. Comp.
• Estimating $\pi(x)$ and related functions under partial RH assumptions, accepted for publication in Math. Comp. preprint version: arXiv:1410.7015
• On the first sign change in Mertens' theorem, 2015, Acta Arith., 171(2): 183-195. preprint version: arXiv:1503.01277
• An improved analytic method for calculating $\pi(x)$, accepted for publication in Manuscripta Mathematica. preprint version: arXiv:1410.7008