Robert P. Langlands

Dimension of spaces of automorphic forms

Author: 
Robert P. Langlands
Last Name: 
Langlands
Journal
Journal: 

Proceedings of the AMS Symposium at Boulder, Colorado

Year: 
1965
Type: 
article

Author's Comments: Although the principal purpose of this paper was to review how the Selberg trace formula is combined with character formulas to calculate the dimension of various spaces of automorphic forms. it is included as a paper on representation theory because the most influential observation in the paper was the description of a possible realization of the discrete series representations on spaces of \(L^2\)-cohomology.

School of Mathematics: 

Euler Products

Author: 
Robert P. Langlands
Journal
Journal: 

Yale Mathematical Monographs

Year: 
1967
Type: 
article
Keywords: 
Eisenstein
MathReview: 
54:7387

Euler Products Cover Page

Editorial comments: The letter to Weil included a number of striking conjectures which eventually changed much of the direction of research in automorphic forms. Some of their consequences were explained in a graduate course given at Princeton in the spring of 1967, and then things were put in a somewhat wider context in a series of lectures at Yale later that Spring. These notes were previously published as the first of the Yale Mathematical Monographs.

School of Mathematics: 

Letter to Godement

Author: 
Robert P. Langlands
Year: 
1967
Type: 
article

Editorial comments: The letter to Weil that saw the birth of the \(L\)-group was written in January, 1967. Somewhat later that same year, Roger Godement asked Langlands to comment on the Ph. D. thesis of Hervé Jacquet. His reply included a number of conjectures on Whittaker functions for both real and \(p\)-adic reductive groups. These were later to be proven, first in the \(p\)-adic case by Shintani for \(\mathrm{GL}_n\) and Casselman Shalika in general, and much later in the real case by a longer succession of people.

School of Mathematics: 

Pages