In Print: ‘Eisenstein Series and Automorphic L-Functions’

Publication title

Eisenstein Series and Automorphic L-Functions

Purdue author

Freydoon Shahidi

Publisher

American Mathematical Society

Publication date

Feb. 28, 2025

About the book (from the publisher)

This book presents a treatment of the theory of L-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory.

This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika’s formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis.

This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.

About the Purdue author

Freydoon Shahidi is a Distinguished Professor Emeritus of Mathematics at Purdue. His research fundamentally advanced the study of L-functions — a tool in advanced mathematics that acts like a sophisticated lens for looking at the properties of numbers, especially prime numbers. Shahidi has received a Guggenheim Fellowship and has also been named an honorary member of the Iranian Mathematical Society, a fellow of the American Mathematical Society, and a fellow of the American Academy of Arts and Sciences.

About the In Print series

To celebrate our faculty’s excellence in scholarship, Purdue Today’s weekly book series highlights faculty expertise across diverse subjects and disciplines. Find out more about the Purdue University Books Initiative and how to suggest a book for the In Print series on the Office of the Provost website.