Sieve Methods for Quantum Unique Ergodicity and General Shifted Sums

PU/IAS NUMBER THEORY
Topic:Sieve Methods for Quantum Unique Ergodicity and General Shifted Sums
Speaker:Roman Holowinsky
Affiliation:Rutgers, The State University of New Jersey and Member, School of Mathematics
Date:Thursday, November 30
Time/Room:4:30pm - 5:30pm/Princeton University, Fine Hall 214

In this talk, I shall introduce a sieve method for bounding the average size of shifted convolution summation terms related to the Quantum Unique Ergodicity Conjecture for a fixed Hecke-Maass cusp form. This bound will be uniform in the spectral parameter provided that standard bounds hold for the symmetric square and symmetric fourth power L-functions at the point s=1. We shall see that the sieve method can be applied to a wide variety of shifted sums, including sums with multiple shifts.