Classical and modern treatments of Riemann zeta function
Loading...
Date
2009.
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009.
Abstract
Tate’s doctoral thesis, Fourier Analysis in Number Fields and Hecke’s Zeta- Functions, on the analytic properties of the class of L-functions introduced by Erich Hecke, is one of the relatively few such dissertations that have become a byword. In it the methods, novel for that time, of Fourier analysis on groups of adeles, were worked out to recover Hecke’s results. In this M.S. thesis, after a brief chapter on the classical treatment of Riemann zeta function, we discuss the local theory, restricted direct products, and the global theory following Tate’s thesis. We compute prime divisors of quadratic fields and quasi-characters of p-adic fields.