Matt Litman (UC Davis)
Date
Tuesday October 25, 20222:00 pm - 3:00 pm
Location
Jeffery Hall, Room 222Number Theory Seminar
Tuesday, October 25th, 2022
Time: 2:00 p.m. Place: Jeffery Hall, Room 222
Speaker: Matt Litman (UC Davis)
Title: Error Approximation for Backwards and Simple Continued Fractions.
Abstract: In this talk, we provide a new framework for studying continued fractions utilizing the backwards continued fraction (BCF). We show an approximation theory for BCFs, the correspondence between continued fractions and their backwards continued fractions counterpart, and illustrate a rich approximation theory for continued fractions (CFs) utilizing the methods of the approximation theory for the backwards continued fractions. In particular, we construct explicit functions that bound the BCF or CF error over any BCF or CF cylinder set, and along the way work out the details to pass seamlessly between the BCF and CF expansion of any real number. This is joint work with Cameron Bjorklund.