Seminars & Colloquia Calendar
Some trigonometric identities associated with the roots of unity
Michael Kiessling, Rutgers University
Date & time: Thursday, 17 February 2022 at 5:00PM - 6:00PM
Abstract: Consider the complete graph whose vertices are the n-th roots of unity in the complex plane. To every edge between a pair of vertices, associate a weight that is a given even non-zero power of the length of the edge. Sum the weights over all pairs of vertices (i.e., over all edges). The result, determined in all generality by Johann Brauchart around 2014 (special cases were known a century before) is always a finite expression in integer powers of n --- thanks to the trivial zeros of Riemann's zeta function. This talk is intended to serve an exciting appetizer to the audience, who hopefully will wish to go for the full meal by reading Johann's papers. Some MAPLE experiments do feature in this talk.
[password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]