Explore a Fields Number Theory Seminar lecture on the non-vanishing of Poincare series, delivered by Kumar Murty from The Fields Institute and University of Toronto. Delve into the intricacies of number theory as Murty examines the relationship between lambda and zeta functions, investigates tau of n, and presents a comprehensive proof of non-vanishing. Learn about kernel functions and their role in the analysis, while gaining insights into the broader implications of Poincare series in mathematical research. Enhance your understanding of advanced number theory concepts through this in-depth, 51-minute presentation from a renowned expert in the field.