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

I will review recent results with Edva Roditty-Gershon and Zeev Rudnick concerning the function-field analogues of conjectures relating to sums of arithmetic functions in short intervals and arithmetic progressions. Our approach uses the connection between L-functions and matrix integrals established by Katz and Sarnak.