7 papers
Resultants, Recursive Formulas and Binet Formulas for Verlinde Sums
Jay Jorgenson, Anders Karlsson, Lejla Smajlović
We study Verlinde sums , which for our purposes are finite sums of trigonometric functions , associated to . In this article we prove the fo…
Evaluating Verlinde sums using spectral graph theory
Jay Jorgenson, Anders Karlsson, Lejla Smajlović
We realize the Verlinde sums , up to an explicit factor, as the values at of the spectral zeta function of a higher-order Laplace operator on the trian…
Diffusion Computation versus Quantum Computation: A Comparative Model for Order Finding and Factoring
Carlos A. Cadavid, Paulina Hoyos, Jay Jorgenson +2
We study a hybrid computational model for integer factorization in which the only non-classical resource is access to an \emph{iterated diffusion process} on a finite graph. Concre…
On a generating function of Niebur-Poincaré series
Kathrin Bringmann, Jay Jorgenson, Lejla Smajlović
Let be a Fuchsian group of the first kind which has a cusp of width one. In this paper, we first consider a generating function formed with t…
The discrete analogue of the Gaussian
Gautam Chinta, Jay Jorgenson, Anders Karlsson +1
This paper illustrates the utility of the heat kernel on as the discrete analogue of the Gaussian density function. It is the two-variable function $K_{\mathbb{Z}}(t,x…
Constructing heat kernels on infinite graphs
Jay Jorgenson, Anders Karlsson, Lejla Smajlović
Let be an infinite, edge- and vertex-weighted graph with certain reasonable restrictions. We construct the heat kernel of the associated Laplacian using an adaptation of the pa…
Effective bounds for Faltings's delta function
J. Jorgenson, J. Kramer
We obtain bounds for the Faltings's delta function for any Riemann surface of genus greater than one. The bounds are in terms of the genus of the surface and two basic quantities c…