11/30/2006

Roman Holowinsky
Institute for Advanced Study

Sieve methods for Quantum Unique Ergodicity and general shifted sums

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.