## The Genesis of the Langlands ProgramRobert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics. |

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### Contents

The Early Langlands Program Personal Reflections | 43 |

Langlands and Turkey | 59 |

Enstitude | 74 |

lhomme derriere le mathematicien | 88 |

Un homme de culture et de nature | 100 |

An Introduction to Langlands Functoriality | 109 |

Langlands Doctoral Thesis | 130 |

The Langlands Spectral Decomposition | 176 |

Automorphic Representations and LFunctions for GLn Dorian Goldfeld and Herve Jacquet | 215 |

Automorphic LFunctions | 275 |

LFunctions Automorphic Forms | 301 |

On Some Early Sources for the Notion of Transfer | 387 |

Robert Langlands Work in Mathematical Physics | 403 |

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abelian algebraic analysis analytic arguments Artin associated automorphic forms automorphic representation Banach space bounds called character class field compact complex conjecture conjugacy class connected consider constant construction continuation converges corresponding decomposition defined definition denote discussion Eisenstein series element elliptic equal established Euler product example existence extension fact factors field finite follows formula functional equation functoriality Galois given gives GL(n Hecke ideas important integral introduced invariant irreducible isomorphism L-functions L-group Langlands later Lecture Lemma limit Math mathematical measure modular motives natural Note notion obtain operators original particular polynomial primes problem proof properties proved questions recall reciprocity reductive result Robert root satisfies semigroup shows space subgroup Theorem theory thesis transfer University unramified vector write