自守形式與Langlands綱領

前言

　　Classical modular forms on the upper half plane with respect to the modular group SL（2， Z） and its congruence subgroups have arisen naturally in number theory， complex analysis， topology， mathematical physics and many other subjects. A natural generalization to other reductive and semisimple linear algebraic groups and their arithmetic subgroups consists of automorphic forms.　　The closely related automorphic representations are basic notions in the celebrated Langlands program， which was proposed by Langlands in the late 1960 and has since revolutionized the fields of number theory， arithmetic algebraic geometry and representation theory. Indeed， many new instances of functoriality have been proved recently， which have led to some spectacular applications.　　A more recent development is the geometric Langlands program， which has had many unexpected applications in algebraic geometry and mathematical physics.　　To help younger mathematicians and non-experts to learn these important fields and their applications， an international conference titled Langlands and Geometric Langlands Program was organized in Guangzhou in June 18-21， 2007.

內容概要

The launch of this Advanced Lectures in Mathematics series is aimed at keeping mathematicians informed of the latest developments in mathematics, as well as to aid in the learning of new mathematical topics by students all over the world.Each volume consists of either an expository monograph or a collection of signifi-cant introductions to important topics. This series emphasizes the history and sources of motivation for the topics under discussion, and also gives an overview of the current status of research in each particular field. These volumes are the first source to which people will turn in order to learn new subjects and to dis-cover the latest results of many cutting-edge fields in mathematics.

書籍目錄

A. W. Knapp: Prerequisites for the Langlands ProgramA. W. Knapp: First Steps with the Langlands ProgramStephen S. Gelbart: Class Field Theory, the Langlands Program,and Its Application to Number TheoryWee Teck Gan: Automorphic Forms and Automorphic Representations.Erez M. Lapid: Introductory Notes on the Trace FormulaSolomon Friedberg: Euler Products and Twisted Euler ProductsXiaoqing Li: Arithmetic Trace Formulas and KloostermaniaD. Shelstad: Tempered Endoscopy for Real Groups II: Spectral Transfer FactorsLi Guo: Algebraic Birkhoff Decomposition and Its Applications

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