Joint IAS/Princeton University Number Theory Seminar

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.