76 citations · 495 across the 37 of their papers we have counts for
9 papers · 1 filter
"Killing Mie Softly": Analytic Integrals for Resonant Scattering States
R. C. McPhedran, B. Stout
We consider integrals of products of Bessel functions and of spherical Bessel functions, combined with a Gaussian factor guaranteeing convergence at infinity. Explicit representati…
Zeros of Lattice Sums: 3. Reduction of the Generalised Riemann Hypothesis to Specific Geometries
Ross C. McPhedran
The location of zeros of the basic double sum over the square lattice is studied. This sum can be represented in terms of the product of the Riemann zeta function and the Dirichlet…
Evaluation and regularization of generalized Eisenstein series and application to 2D cylindrical harmonic sums
Parry Y. Chen, Michael J. A. Smith, Ross C. McPhedran
In the study of periodic media, conditionally convergent series are frequently encountered and their regularization is crucial for applications. We derive an identity that regulari…
Zeros of Lattice Sums: 2. A Geometry for the Generalised Riemann Hypothesis
R. C. McPhedran
The location of zeros of the basic double sum over the square lattice is studied. This sum can be represented in terms of the product of the Riemann zeta function and the Dirichlet…
Zeros of Lattice Sums: 1. Zeros off the Critical Line
Ross C. McPhedran
Zeros of two-dimensional sums of the Epstein zeta type over rectangular lattices of the type investigated by Hejhal and Bombieri in 1987 are considered, and in particular a sum fir…
The Riemann Hypothesis for Dirichlet Functions
Ross C. McPhedran
This paper studies the connections between the zeros and their distribution functions for two particular Dirichlet functions: the Riemann zeta function, and the Catalan beta fu…