Patrick Ingram : Finiteness of solutions to certain differential and difference equations

Posted by Ronnie Nagloo , part of the Unlikely Intersections Seminar.

At

Jan. 24, 2023, 2 p.m.

In

636 SEO

Abstract

A result of Malmquist establishes the rationality of solutions to non-Riccati differential equations of the form f’=R(z,f), where R is a rational function, while an analogous result of Yanagihara places restrictions on solutions to the difference equation f(z+1)=R(z,f). In this talk we will look at the problem of bounding the number of solutions to such equations, and if time allows we will also mention an improvement to Nevanlinna’s Second Main Theorem for solutions to difference equations.