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Course Descriptions

16:640:573 - Special Topics Number Theory

Fall 2017

Henryk Iwaniec


Spectral theory of automorphic forms


Henryk Iwaniec, Spectral Methods of Automorphic Forms, AMS Grad.Stud. Vol.53, 2002


Good knowledge of functional analysis and complex function theory will be helpful


This will be a one semester course on automorphic forms from analytic point of view. The main topics are:

-spectral decomposition

-trace formula

-sums of Kloosterman sums

-distribution of eigenvalues of the Laplace operator (Weyl's law, exceptional eigenvalues)

-distribution of Hecke eigenvalues

-hyperbolic lattice point problems

-application to equidistribution of roots of congruences

Sections Taught This Semester:

For more information on instructors and sections for this course, please see our Teaching Schedule Page

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530