Pub Date : 2021-07-31DOI: 10.1017/9781108591218.019
D. Goldfeld, Hervé Jacquet
{"title":"Automorphic Representations and L-Functions for GL(n)","authors":"D. Goldfeld, Hervé Jacquet","doi":"10.1017/9781108591218.019","DOIUrl":"https://doi.org/10.1017/9781108591218.019","url":null,"abstract":"","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128483060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-31DOI: 10.1017/9781108591218.013
C. Lévesque
{"title":"Robert P. Langlands: l’homme derrière le mathématicien","authors":"C. Lévesque","doi":"10.1017/9781108591218.013","DOIUrl":"https://doi.org/10.1017/9781108591218.013","url":null,"abstract":"","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116583504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-31DOI: 10.1017/9781108591218.006
{"title":"Langlands As Mentor","authors":"","doi":"10.1017/9781108591218.006","DOIUrl":"https://doi.org/10.1017/9781108591218.006","url":null,"abstract":"","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133767651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-31DOI: 10.1017/9781108591218.020
F. Shahidi
{"title":"Automorphic L-Functions","authors":"F. Shahidi","doi":"10.1017/9781108591218.020","DOIUrl":"https://doi.org/10.1017/9781108591218.020","url":null,"abstract":"","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116690197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-31DOI: 10.1017/9781108591218.022
Diana Shelstad
{"title":"On Some Early Sources for the Notion of Transfer in Langlands Functoriality: Part I An Overview with Examples","authors":"Diana Shelstad","doi":"10.1017/9781108591218.022","DOIUrl":"https://doi.org/10.1017/9781108591218.022","url":null,"abstract":"","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132808824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-31DOI: 10.1017/9781108591218.016
James Arthur
The Principle of Functoriality has long been regarded as the centre of the Langlands Program. More recently, it has had to share the spotlight with Reciprocity, Langlands’ conjecture that relates automorphic representations with motives from algebraic geometry. However, the two principles are closely related, and in any case, Reciprocity came at the end of the decade that followed the years 1960–1967 that are the focus of this volume. Functoriality famously had its roots in the seventeen-page letter that Langlands gave to André Weil in 1967 [L2]. He wrote some of the details shortly afterwards in the article he dedicated to Salomon Bochner [L3]. It represented a very different direction for Langlands after his monumental volume [L1] on Eisenstein series, which was largely analysis. Langlands credits Bochner, an analyst himself, with directing him towards number theory, especially, I believe, class field theory and its long-sought nonabelian generalization. There are several ways to introduce functoriality to a general reader. One is as a series of identities (reciprocity laws) that relate families of conjugacy classes c = {cp : p N}
功能原理一直被认为是朗兰兹纲领的核心。最近，它不得不与朗兰兹(Langlands)提出的自同构表示与代数几何的动机联系起来的“互易性”(Reciprocity)共同受到关注。然而，这两个原则是密切相关的，在任何情况下，互惠是在1960-1967年之后的十年结束时出现的，这是本卷的重点。众所周知，功能性起源于1967年朗兰兹给安德烈·韦尔的一封长达17页的信[2]。不久之后，他在一篇献给所罗门·博希纳的文章中写下了一些细节。它代表了朗兰兹在他关于爱森斯坦系列的巨著[1]之后的一个非常不同的方向，这主要是分析。朗兰兹认为，博奇纳本人也是一位分析师，是他引导他走向数论，尤其是我相信的阶级场论及其长期寻求的非阿贝尔推广。有几种方法可以向普通读者介绍功能。一种是将共轭类c = {cp: p N}的族联系起来的一系列恒等式(互易律)。
{"title":"An Introduction to Langlands Functoriality","authors":"James Arthur","doi":"10.1017/9781108591218.016","DOIUrl":"https://doi.org/10.1017/9781108591218.016","url":null,"abstract":"The Principle of Functoriality has long been regarded as the centre of the Langlands Program. More recently, it has had to share the spotlight with Reciprocity, Langlands’ conjecture that relates automorphic representations with motives from algebraic geometry. However, the two principles are closely related, and in any case, Reciprocity came at the end of the decade that followed the years 1960–1967 that are the focus of this volume. Functoriality famously had its roots in the seventeen-page letter that Langlands gave to André Weil in 1967 [L2]. He wrote some of the details shortly afterwards in the article he dedicated to Salomon Bochner [L3]. It represented a very different direction for Langlands after his monumental volume [L1] on Eisenstein series, which was largely analysis. Langlands credits Bochner, an analyst himself, with directing him towards number theory, especially, I believe, class field theory and its long-sought nonabelian generalization. There are several ways to introduce functoriality to a general reader. One is as a series of identities (reciprocity laws) that relate families of conjugacy classes c = {cp : p N}","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121914661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-31DOI: 10.1017/9781108591218.005
S. Gelbart
{"title":"The Early Langlands Program – Personal Reflections","authors":"S. Gelbart","doi":"10.1017/9781108591218.005","DOIUrl":"https://doi.org/10.1017/9781108591218.005","url":null,"abstract":"","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116844273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-31DOI: 10.1017/9781108591218.004
J. Mueller
This chapter serves as an introduction to the volume as a whole, and it is aimed at a general mathematical audience. Our presentation of the early life and work of Robert Langlands, creator and founder of the Langlands program, is narrated, to a large extent, by Langlands himself. We focus on two of Langlands’ major discoveries: automorphic L-functions and the functoriality conjecture. Langlands’ desire to communicate his excitement about his newly discovered objects resulted in his famous letter to André Weil in January 1967, and the Langlands program was launched soon afterwards. Section 1.2 of this chapter focuses on Langlands’ early years, from 1936 to 1960, and the material is taken from an interview given by Langlands to a student, Farzin Barekat, at the University of British Columbia (UBC), Langlands’ alma mater, in the early 2000s. A copy of this interview is available on Langlands’ website at http://publications.ias.edu/rpl/. Section 1.3 is an overview of Langlands’ early work and professional life from 1960 to 1967. It contains a brief descriptive account of the essential events that led him to his discoveries of automorphic L-functions and the functoriality conjecture. Our source material in this part is taken largely from our correspondence and interviews with Langlands himself over the past few years. Those correspondence can also be found on Langlands’ website.
{"title":"A Glimpse at the Genesis of the Langlands Program","authors":"J. Mueller","doi":"10.1017/9781108591218.004","DOIUrl":"https://doi.org/10.1017/9781108591218.004","url":null,"abstract":"This chapter serves as an introduction to the volume as a whole, and it is aimed at a general mathematical audience. Our presentation of the early life and work of Robert Langlands, creator and founder of the Langlands program, is narrated, to a large extent, by Langlands himself. We focus on two of Langlands’ major discoveries: automorphic L-functions and the functoriality conjecture. Langlands’ desire to communicate his excitement about his newly discovered objects resulted in his famous letter to André Weil in January 1967, and the Langlands program was launched soon afterwards. Section 1.2 of this chapter focuses on Langlands’ early years, from 1936 to 1960, and the material is taken from an interview given by Langlands to a student, Farzin Barekat, at the University of British Columbia (UBC), Langlands’ alma mater, in the early 2000s. A copy of this interview is available on Langlands’ website at http://publications.ias.edu/rpl/. Section 1.3 is an overview of Langlands’ early work and professional life from 1960 to 1967. It contains a brief descriptive account of the essential events that led him to his discoveries of automorphic L-functions and the functoriality conjecture. Our source material in this part is taken largely from our correspondence and interviews with Langlands himself over the past few years. Those correspondence can also be found on Langlands’ website.","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131038406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-31DOI: 10.1017/9781108591218.014
Claude Pichet
{"title":"Un homme de culture et de nature","authors":"Claude Pichet","doi":"10.1017/9781108591218.014","DOIUrl":"https://doi.org/10.1017/9781108591218.014","url":null,"abstract":"","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116838377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.1017/9781108591218.017
D. W. Robinson
This is a draft version of an invited article for a forthcoming book `The genesis of Langlands Program', eds. Julia Mueller and Freydoon Shahidi, which will be published in the London Mathematics Society Lecture Notes Series. It gives a description of the background and content of the unpublished doctoral thesis of Robert Langlands with many alternative explanations and proofs of the principal results.
{"title":"In the Beginning: Langlands’ Doctoral Thesis","authors":"D. W. Robinson","doi":"10.1017/9781108591218.017","DOIUrl":"https://doi.org/10.1017/9781108591218.017","url":null,"abstract":"This is a draft version of an invited article for a forthcoming book `The genesis of Langlands Program', eds. Julia Mueller and Freydoon Shahidi, which will be published in the London Mathematics Society Lecture Notes Series. It gives a description of the background and content of the unpublished doctoral thesis of Robert Langlands with many alternative explanations and proofs of the principal results.","PeriodicalId":306197,"journal":{"name":"The Genesis of the Langlands Program","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124678288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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