Abstract:
John Tate in his doctoral dissertation, “Fourier Analysis on Number Fields and Hecke’s Zeta Function”, established the meromorphic continuation and functional equation of Hecke’s Zeta Function over a number field using methods of harmonic analysis on the ad`ele ring of the number field. The theory in Tate’s thesis can be extended to L-functions that are attached to Hecke characters - which are id`ele class group characters. In this thesis, we study the necessary background and explore the key concepts to provide a comprehensive exposition of Tate’s work. Further, we continue to study Hecke characters - the associated L-functions along with the arithmetic aspects of these L-functions.
