By Kathrin Bringmann, Yann Bugeaud, Titus Hilberdink, Jurgen Sander

This booklet arose from classes given on the foreign summer season college equipped in August 2012 via the quantity idea staff of the dep. of arithmetic on the college of Würzburg. It involves 4 primarily self-contained chapters and offers contemporary examine effects highlighting the powerful interaction among quantity conception and different fields of arithmetic, equivalent to combinatorics, sensible research and graph conception. The publication is addressed to (under)graduate scholars who desire to become aware of numerous facets of quantity conception. Remarkably, it demonstrates how simply you'll be able to strategy frontiers of present study in quantity concept by way of user-friendly and simple analytic methods.

Kathrin Bringmann offers an creation to the speculation of modular types and, specifically, so-called Mock theta-functions, a subject matter which were untouched for many years yet has got a lot realization within the final years. Yann Bugeaud is worried with expansions of algebraic numbers. the following combinatorics on phrases and transcendence idea are mixed to derive new info at the series of decimals of algebraic numbers and on their persisted fraction expansions. Titus Hilberdink stories on a up to date and really unforeseen method of severe values of the Riemann zeta-function by way of use of (multiplicative) Toeplitz matrices and useful research. ultimately, Jürgen Sander provides an creation to algebraic graph conception and the influence of quantity theoretical equipment on basic questions about the spectra of graphs and the analogue of the Riemann speculation.