## Number Theory, Dynamical Systems and Statistical Mechanics (1998)

Citations: | 8 - 2 self |

### BibTeX

@MISC{Knauf98numbertheory,,

author = {Andreas Knauf},

title = {Number Theory, Dynamical Systems and Statistical Mechanics},

year = {1998}

}

### OpenURL

### Abstract

In these lecture notes connections between the Riemann zeta function, motion in the modular domain and systems of statistical mechanics are presented. 1 Introduction Counting was the earliest mathematical activity. Number theory thus was among the first subjects of mathematics. It was shown by Euclid that every integer n 2 N has a unique factorization n = Y p2P p ff p (1) in terms of the primes P ae N , and a class of rings like Z sharing this property thus bears his name. To some extent the beauty of number theory seems to be related to the contradiction between the simplicity of the integers and the complicated structure of the primes, their building blocks. This has always attracted people. A nonrepresentative example is the following, from a book by Sacks: He describes a dialogue between twins: "John would say a number --- a six-figure number. Michael would catch the number, nod, smile and seem to savour it. Then he, in turn, would say another six-figure number, and now it ...