The arithmetic of power series

Abstract: Abstract: 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 $\mathrm{SL}_2(\mathbf{Z})$ are determined by congruence conditions. This talk is based on joint work with Vesselin Dimitrov and Yunqing Tang.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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