Date/Time Date(s) - 20/10/202312:30 pm - 1:30 pm
Location: HH 312
Speaker: Adele Pagdett (McMaster University)
Title: Some equations involving the Gamma function
Abstract: The Gamma function extends factorials to complex numbers and thus appears in many different mathematical contexts. Though Gamma is a transcendental holomorphic function, it satisfies several important functional equations. A first step toward understanding its model theory would be to study any other algebraic properties it may possess. In this talk, I will present recent work with Sebastian Eterovic in which we prove certain systems of equations involving addition, multiplication, and the Gamma function must have infinitely many solutions in the complex numbers. Similar results have been obtained for periodic functions such as exp, the modular j function, and others. We combine techniques established for these functions with new ideas in order to study Gamma, a non-periodic function. An immediate corollary is that the Gamma function has infinitely many periodic points of every period.