Weyl's Sums for Roots of quadratic Congruences

JOINT IAS/PU NUMBER THEORY SEMINAR
Topic:Weyl's Sums for Roots of quadratic Congruences
Speaker:Henryk Iwaniec
Affiliation:Rutgers, The State University of New Jersey
Date:Thursday, December 16
Time/Room:4:30pm - 5:30pm/Fine Hall -- 214

It is known that the roots of congruences for a fixed irreducible quadratic polynomial are equidistributed. This statement translates to getting cancellation in the corresponding sum of Weyl's sums. In a recent work by W. Duke, J. Friedlander and H. Iwaniec we succeeded to get cancellation (so also the equidistribution) in very short sums of Weyl's sums relatively to the discriminant. The spectral theory of metaplectic automorphic forms is the basic tool, of which some special aspects will be the subject of this talk. Numerous applications of the result will be also discussed.