A Survey of the Selberg Class of L-Functions, Part I

摘要

This is the first part of a survey of the axiomatic class of L-functions introduced by Selberg [32]. Our aim is to give a rather complete overview of the results, conjectures and problems which are related to the Selberg class. Apart from very few exceptions, we do not give proofs of the results. However, we provide very brief indications of the arguments, as well as motivations for conjectures and problems. While the conjectures are generally expected to be difficult, the level of the problems is not at all homogeneous: some of them should not be difficult, while others are probably very hard.