====== Wladimir de Azevedo Pribitkin (Haverford College) ======

====== Kloosterman Sums ======

===== Abstract for the Combinatorics and Number Theory Seminar 2002 November 12 =====

Kloosterman sums arise naturally in connection with certain modular forms called Poincaré series. In this talk I will expound their historical origin and explain their relevance in the context of the Linnik-Selberg Conjecture. In particular, I will present a recent refinement of mine for the remainder term that appears in the Petersson inner product of two nonholomorphic Poincaré series.