Japanese version
In 23 Oct.2011 Mathematical Physics Seminar the second I gave a talk about "Zeta Functions and Statistical Dynamics," And now as part III "3,Various zeta functions" is posted. I mention congruent zeta and Selberg zeta and various conjecture of quantum chaos. My talk is related Mr. Konishi's at the first seminar.
The contents are the following :
0,Introduction
1,Distribution of prime numbers (Riemann zeta function)
2,The origin of conjunction of Phys. and NT.
3,Various zeta functions
4,Statistical Dynamics and Zeta Functions
App. A story of (Thermo) Statistical Dynamics
Zeta Functions and Statistical Dynamics III
The Minakshisandaram-Pleijel zeta function is very important.
ReplyDeleteIt has impact on the zeta function of operators and the boundary value problems as the heat kernel. And it has led to the Ray-Singer torsion. The zeta function of normalization by Hawking also relates to this.
Nov. 3 2012