Hester Graves (Center for Computing Sciences)
Date
Friday October 18, 20242:30 pm - 3:30 pm
Location
234 JEFFERY HALLMath & Stats Department Colloquium
Friday, October 18, 2024
Time: 2:30 p.m. Place: Jeffery Hall, Room 234
Speaker: Hester Graves (Center for Computing Sciences)
Title: The Minimal Euclidean Function on the Gaussian Integers
Abstract: Motzkin proved that every Euclidean domain $R$ has a minimal Euclidean function, $\phi_R$ . He showed that when $R = \mathbb{Z}$, the minimal function is $\phi_{\mathbb{Z}} (x) =\ log 2_ |x|$. For over seventy years, $\phi_{\mathbb{Z}}$ was the only example of an explicitly-computed minimal function in a number field. We give the first explicitly-computed minimal function in a non-trivial number field, $\phi_{\mathbb{Z}[i]}$ . The proof introduces a new way to visualize quotients $\mathbb{Z}[i]$. This talk is accessible to undergraduates.