自守形式与L-函数

内容概要

刘建亚，男，1964年生于河北固安，汉族，中共党员，博士、教授、博士生导师，1984年获河北师范大学学士学位，1992年、1995年分别获山东大学硕士、博士学位，1996~1998在香港大学从事博士后研究。现任山东大学数学学院院长、山东省数学学会理事长、Advances in Mathematics of Communications杂志主编、东北数学杂志编委。

书籍目录

《自守形式与l-函数(精装)》

l-functions and functoriality

james w. cogdell

i l-functions for gl(n) and converse theorems

1 modular forms and automorphic representations

2 l-functions for gln and converse theorems

ii l-functions via eisenstein series

3 the origins: langlands

4 the method: langlands-shahidi

5 the results: shahidi

iii functoriality

6 langlands conjectures and functoriality

7 the converse theorem and functoriality

8 symmetric powers and applications

references

twisted hilbert modular l-functions and spectral theory

gergely harcos

1 lecture one: some quadratic forms

2 lecture two: more quadratic forms

3 lecture three: preliminaries from number theory

4 lecture four: subconvexity of twisted l-functions

acknowledgments

references

the voronoi formula for the triple divisor function

xiaoqing li

1 introduction

2 proof of the main theorem

acknowledgments

references

linnik's ergodic method and the hasse principle for ternary

quadratic forms

philippe michel

1 foreword

2 integral quadratic forms

3 the hasse principle

4 quadratic forms over lattices

5 equidistribution on adelic quotient

6 properties of the adeles

7 the hasse integral principle and equidistribution of adelic orbits

8 the ergodic method

references

automorphic periods and representation theory

andre reznikov

1 automorphic representations and frobenius reciprocity

2 bounds on periods and representation theory

acknowledgments

references

eisenstein series, l-functions and representation theory

freydoon shahidi

1 preliminaries

2 l-groups, l-functions and generic representations

3 eisenstein series and intertwining operators;the constant term

4 constant term and automorphic l-functions

5 examples

6 local coefficients, nonconstant term and the crude functional equation

7 the main induction, functional equations and multiplicativity

8 twists by highly ramified characters, holomorphy and boundedness

9 examples of functoriality with applications

10 applications to representation theory

references

lecture notes on some analytic properties of automorphic

l-functions for sl2(z)

yangbo ye

1 introduction

2 an integral representation and functional equation

3 a converse theorem

4 the phragmen-lindelof principle and convexity

5 the rankin-selberg theory

references

作者简介

CIMPA-UNESCO-CHINA暑期学校“自守形式与L-函数”于2010年8月1日至14日在山东大学威海校区举办，该国际暑期学校受联合国教科文组织资助，邀请的演讲人都是本领域著名的专家。本书汇集了这次暑期学校以下演讲人的讲义：J．Cogdell，G．Harcos，李小青，P.Michel，A．Reznikov，F.Shahidi以及叶扬波。本书涵盖自守形式、L-函数、谱理论及表示理论等方面的内容，既给出了自守形式与L-函数很好的介绍，也指出了其算术应用。本书不仅是本领域专家们有价值的参考书，也是研究生开展研究时极好的入门书。

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