Departmental Colloquium

Event Information The Arithmetic of Power Series
16:10 on Wednesday March 08, 2023
17:00 on Wednesday March 08, 2023
BA6183, Bahen Center, 40 St. George St.
Frank Calegari

University of Chicago

A function of a complex variable P(z) which is holomorphic around z=0 has a power series expansion P(z)=sum a_n z^n. Suppose that the a_n are all integers: what restrictions does that place on the function P(z)? We explore the relationship between this problem to questions in complex analysis, number theory, and to Klein’s famous observation that not all finite index subgroups of SL_2(Z) are determined by congruence conditions.