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Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Gisbert Wüstholz and Clemens Fuchs (eds)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.001.0001
Subject:
Mathematics, Geometry / Topology

This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the ... More


L-Functions

Günter Harder and A. Raghuram

in Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions: (AMS-203)

Published in print:
2019
Published Online:
September 2020
ISBN:
9780691197890
eISBN:
9780691197937
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691197890.003.0007
Subject:
Mathematics, Number Theory

This chapter turns to L-functions. It first covers motivic and cohomological L-functions. There is a well-known conjectural dictionary between cohomological cuspidal automorphic representations of ... More


Introduction

Gisbert Wüstholz and Clemens Fuchs (eds)

in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.003.0001
Subject:
Mathematics, Geometry / Topology

This introductory chapter provides an overview of the three topics discussed in this book: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and ... More


Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang

Ziyang Gao, Rafael von Känel, and Lucia Mocz

in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.003.0004
Subject:
Mathematics, Geometry / Topology

This chapter explores Shou-Wu Zhang's minicourse on Faltings heights and L-functions. It essentially consists of three parts. The first part discusses conjectures and results in the literature which ... More


Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions: (AMS-203)

Anantharam Raghuram and Günter Harder

Published in print:
2019
Published Online:
September 2020
ISBN:
9780691197890
eISBN:
9780691197937
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691197890.001.0001
Subject:
Mathematics, Number Theory

This book studies the cohomology of locally symmetric spaces for GL(N) where the cohomology groups are with coefficients in a local system attached to a finite-dimensional algebraic representation of ... More


Random matrices and number theory: some recent themes

Jon P. Keating

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The aim of this chapter is to motivate and describe some recent developments concerning the applications of random matrix theory to problems in number theory. The first section provides a brief and ... More


Introduction

Günter Harder and A. Raghuram

in Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions: (AMS-203)

Published in print:
2019
Published Online:
September 2020
ISBN:
9780691197890
eISBN:
9780691197937
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691197890.003.0001
Subject:
Mathematics, Number Theory

This introductory chapter presents the general principle that the cohomology of arithmetic groups and the L-functions L(s, π‎, r) attached to irreducible “pieces” π‎ have a strong symbiotic ... More


The Archimedean Intertwining Operator for GLN

Uwe Weselmann

in Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions: (AMS-203)

Published in print:
2019
Published Online:
September 2020
ISBN:
9780691197890
eISBN:
9780691197937
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691197890.003.0009
Subject:
Mathematics, Number Theory

This chapter generalizes an identity conjectured by G. Harder and proved by D. Zagier from the case of GL3(ℝ)-representations to the case of general GLN(ℝ)-representations. These are useful in ... More


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