# 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 PhD student of Prof. Dr. Franke and I am interested in analytic algorithmic number theory. I am particularly interested in questions concerning prime-counting and zero-counting 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, to appear in Math. Comp., preprint at arXiv:1308.6704
• A Brun-Titchmarsh Inequality for weighted sums over prime numbers, 2014, to appear in Acta Arithmetica, preprint at arXiv:1410.7561

## Preprints

• (with J. Franke, T. Kleinjung and A. Jost) A practical analytic method for calculating $\pi(x)$ . Preprint available on demand.
• A practical analytic method for calculating $\pi(x)$ II. arXiv:1410.7008
• Estimating $\pi(x)$ and related functions under partial RH assumptions. arXiv:1410.7015