# The Looman-Menchoff Theorem.

Speaker: Anwoy Maitra.

Date: 3 February, 2015 (Tuesday)

Time: 09:15 pm – 10:15 pm

Venue: Lecture Hall I, Department of Mathematics

Abstract: In this talk, we will present a full proof of a result one hears about often during a first course in complex analysis, but a proof of which is very rarely given. It is the Looman-Menchoff theorem, which asserts that if $D$ is an open subset of $\mathbb{C}$ and if $f: D \to \mathbb{C}$ is a continuous function such that all the first order partial derivatives of $f$ exist and such that the Cauchy-Riemann equations are satisfied, then $f$ is holomorphic. This result, while simple-sounding, is quite nontrivial!

Area: Complex Analysis