Series Title
" Analysis and arithmetic on locally symmetric manifolds and appliations "
Abstract

Lecture 1
The Ramanujan Conjectures (spectra)
Tuesday, Mar 7, 2 PM, MS 6627

Lecture 2
The Ramanujan Conjectures (periods)
Wednesday, Mar 8, 2 PM, MS 6627

Lecture 3
Applications to sieving for primes on varieties
Thursday, Mar 9, 2 PM, MS 6627

Warmup Seminars to be announced in week of 2/27-3/3

Background reading recommended by Professor Sarnak:

a. Notes on the generalized Ramanujan Conjectures
b. Spectra of hyperbolic surfaces

These may be downloaded from the speaker's website: www.math.princeton.edu/sarnak/ look under pre- prints and letters.

For applications, the paper by Duke, Sarnak and Rudnick Density of integer points on affine homogeneous varieties in Duke Math Journal 71 (1993) 143-179 is useful

In addition to the above survey articles by himself, Professor Sarnak has strongly recommended the following approachable papers by A. Selberg as preparation for the lectures by Professor Sarnak:

1) Paper 19 in his collected works Vol 1 ,page 363 to 366 "On an elementary method in the theory of primes"
2)Page 506 paper 33, "On the estimation of Fourier Coefficients of Modular Forms"

The first is a very elementary and important paper in sieve theory. It shows how to give sharp upper bounds for counting say twin primes. No prerequisites are needed.