The resolvent kernel on the discrete circle and twisted cosecant sums

Jay Jorgenson, Anders Karlsson, Lejla Smajlović

Let $X_m$ denote the discrete circle with $m$ vertices. For $x,y\in X_m$ and complex $s$, let $G_{X_m,{\chi }_{\beta }}(x,y;s)$ be the resolvent kernel associated to the combinatorial Laplaci…