Heinz Huber und das Längenspektrum

Abstract

This is a historical article about the discovery of the length spectrum of a compact Riemann surface. It begins with Euler’s product formula for the prime numbers from 1737, proceeds to Riemann’s zeta function and then focusses on the theorems about length and eigenvalue spectra that were discovered by Heinz Huber in the 1950s. Emphasis is given to the comparison of Wiener’s proof of the prime number theorem with Huber’s proof of the asymptotic formula for the lengths of closed geodesics. The history ends with a brief outlook to current research.