Second Moment of the GL_3 Standard L-function on the Critical Line

Explore the intricacies of the second moment of the GL_3 standard L-function on the critical line in this advanced number theory lecture. Delve into the historical context of moment calculations for the Riemann zeta function, understanding why the sixth moment remains an open problem. Examine how this challenge relates to the second moment of a GL_3 Eisenstein series and its cusp form variants. Learn about recent advancements made by the speaker and collaborators in obtaining a nontrivial bound on this second moment. Discover the practical applications of this research, including improvements to the Rankin-Selberg problem. Gain insights into cutting-edge mathematical techniques and their implications for number theory and related fields.

Second Moment of the GL_3 Standard L-function on the Critical LineMatthew Young