17 citations · 42 across the 15 of their papers we have counts for
19 papers
On a generating function of the basis of weakly holomorphic functions on an elliptic curve
Joshua S. Friedman, Jay Jorgenson, Lejla Smajlović
Let $\Gz$ be a cofinite Fuchsian group whose quotient $\Gz\backslash\HH$ has genus one and a single cusp, normalized to be at with width one. Let $\Xg$ be its smooth compa…
Asymptotics of the spectral determinant of the weighted Laplacian for a sequence of compact Riemann surfaces of infinitely growing volume
Jay Jorgenson, Lejla Smajlovic, Polyxeni Spilioti
Let be a triple consisting of a smooth, compact hyperbolic Riemann surface of genus , and an dimensional unitary multiplier system of admissible weight …
An explicit construction of heat kernels and Green's functions in measure spaces
Palle Jorgensen, Jay Jorgenson, Lejla Smajlovic
We explicitly construct a heat kernel as a Neumann series for certain function spaces, such as , , and Hilbert spaces, associated to a locally compact Hausdorff space…
Determinants of twisted Laplacians and the twisted Selberg zeta function
Jay Jorgenson, Lejla Smajlovic, Polyxeni Spilioti
Let be an orbisurface, meaning a compact hyperbolic Riemann surface possibly with a finite number of elliptic points, and let denote its unit tangent bundle. We consider…
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…
On the functional equation of twisted Ruelle zeta function and Fried's conjecture
Jay Jorgenson, Min Lee, Lejla Smajlovic
Let be a finite volume hyperbolic Riemann surface with arbitrary signature, and let be an arbitrary -dimensional multiplier system of weight . Let be the ass…
Kronecker limit functions and an extension of the Rohrlich-Jensen formula
James Cogdell, Jay Jorgenson, Lejla Smajlovic
In 1984 Rohrlich proved a modular analogue of Jensen's formula. Under certain conditions, the Rohrlich-Jensen formula expresses an integral of the log-norm of…
Evaluating the Mahler measure of linear forms via Kronecker limit formulas on complex projective space
James Cogdell, Jay Jorgenson, Lejla Smajlovic
In Cogdell et al., \it LMS Lecture Notes Series \bf 459, \rm 393--427 (2020), \rm the authors proved an analogue of Kronecker's limit formula associated to any divisor …
Spectral construction of non-holomorphic Eisenstein-type series and their Kronecker limit formulas
James Cogdell, Jay Jorgenson, Lejla Smajlovic
Let be a smooth, compact, projective Kähler variety and be a divisor of a holomorphic form , and assume that is smooth up to codimension two. Let be a Kähler for…
Super-zeta functions and regularized determinants associated to cofinite Fuchsian groups with finite-dimensional unitary representations
Joshua S. Friedman, Jay Jorgenson, Lejla Smajlovic
Let be a finite volume, non-compact hyperbolic Riemann surface, possibly with elliptic fixed points, and let denote a finite dimensional unitary representation of the funda…
Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps
Joshua S. Friedman, Jay Jorgenson, Lejla Smajlovic
Let denote a sequence of complex numbers and assume that that the counting function $#\{λ_{k} \in Λ: | λ_{k}| < T\} =O(T^{n})$ for some integer . From Hadamard's…
An evaluation of the central value of the automorphic scattering determinant
Joshua S. Friedman, Jay Jorgenson, Lejla Smajlovic
Let be a finite volume, non-compact hyperbolic Riemann surface, possibly with elliptic fixed points, and let denote the automorphic scattering determinant. From the know…
The determinant of the Lax-Phillips scattering operator
Joshua S. Friedman, Jay Jorgenson, Lejla Smajlovic
Let denote a finite volume, non-compact Riemann surface without elliptic points, and let denote the Lax-Phillips scattering operator. Using the superzeta function approach…
Certain aspects of holomorphic function theory on some genus zero arithmetic groups
Jay Jorgenson, Lejla Smajlovic, Holger Then
There are a number of fundamental results in the study of holomorphic function theory associated to the discrete group PSL(2,Z) including the following statements: The ring of holo…
On the wave representation of hyperbolic, elliptic, and parabolic Eisenstein series
Jay Jorgenson, Anna-Maria von Pippich, Lejla Smajlovic
We develop a unified approach to the construction of the hyperbolic and elliptic Eisenstein series on a finite volume hyperbolic Riemann surface. Specifically, we derive expression…
Applications of Kronecker's limit formula for elliptic Eisenstein series
Jay Jorgenson, Anna-Maria von Pippich, Lejla Smajlovic
We develop two applications of the Kronecker's limit formula associated to elliptic Eisenstein series: A factorization theorem for holomorphic modular forms, and a proof of Weil's…
Kronecker's limit formula, holomorphic modular functions and -expansions on certain moonshine groups
Jay Jorgenson, Lejla Smajlović, Holger Then
For any square-free integer such that the "moonshine group" has genus zero, the Monstrous Moonshine Conjectures relate the Hauptmoduli of to certain McKay…
On the distribution of zeros of the derivative of Selberg's zeta function associated to finite volume Riemann surfaces
Jay Jorgenson, Lejla Smajlovic
W. Luo has investigated the distribution of zeros of the derivative of the Selberg zeta function associated to compact hyperbolic Riemann surfaces. In essence, the main results in…
On the distribution of eigenvalues of Maass forms on certain moonshine groups
Jay Jorgenson, Lejla Smajlović, Holger Then
In this paper we study, both analytically and numerically, questions involving the distribution of eigenvalues of Maass forms on the moonshine groups , where is a s…