Distribution of Zeros, Eigenvalues and Eigenfunctions in Number Theory

Explore the statistical laws governing zeta functions and automorphic forms in this mathematical lecture by Peter Sarnak from the Simons Foundation. Examine the distribution patterns of zeros, eigenvalues, and eigenfunctions within number theory, focusing on how these statistical principles manifest in numerical observations. Investigate the connection between these distribution laws and their significant impact on the extremal properties of arithmetical invariants. Gain insights into the universal statistical phenomena that emerge in number-theoretic contexts and understand how computational evidence supports theoretical predictions about these fundamental mathematical objects.