Analysis, Spectra and Number Theory, a Conference in Honor of Peter Sarnak’s 61st Birthday

In the lecture, we will describe several applications of the theory of trace functions (Frobenius trace functions associated to $\ell$-adic sheaves on the affine line over $\mathbb{F}_q$) to analytic number theory. This is a report of several recent works made by and with a variety of people including V. Blomer, E. Kowalski, E. Fouvry, D. Milicevic, W. Savin and D. H. J. Polymath.