Elementary Theory of L-Functions I

Abstract

In this first chapter we will define and describe, in a roughly chronological order from the time of Euler to that of Hecke, some interesting classes of holomorphic functions with strange links to many aspects of number theory. Later chapters will explain how at least some of the mysterious aspects are understood today. But it should be emphasized that there are still many points that are not fully explained, even in a very sketchy, philosophical way.