Charles Alley : The Rogers-Ramanujan Continued Fraction: An Interesting Individual

Posted by Dylon Chow , part of the Graduate Number Theory Seminar.

At

Feb. 18, 2015, 3 p.m.

In

SEO 512

Abstract

C.L. Siegel said, "The mathematical universe is inhabited not only by important species but also by interesting individuals." In this talk I will discuss the Rogers-Ramanujan continued fraction, $r(t) = q^{1/5}/1+q/1+q^2/1+q^3/1+... $ where $q=e^{2\pi i t}$. This classical function has many interesting properties, which I will discuss. I will present results from the survey paper by W. Duke, "Continued Fractions and Modular Functions", which can be found here: http://www.math.ucla.edu/~wdduke/preprints/bams4.pdf