Related papers: On the Euclidean Version of the Photon Number Inte…
Various integrals over elliptic integrals are evaluated as couplings on spheres, resulting in some integral and series representations for the mathematical constants $\pi$, $G$ and $\zeta(3)$.
In this talk we discuss the interplay of two elliptic curves, which occur in different sub-sectors of Feynman integrals. We analyse a particular Feynman integral depending on two elliptic curves and derive an associated differential…
In this paper we shall investigate the problem of the representation of the number of integral points of an elliptic curve modulo a prime number p. We present a way of expressing an exponential sum which involves polynomials of third…
We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of $m^2=n^2+nl+l^2$.
We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process $\pi^-\gamma \to \pi^-\pi^0\pi^0$. At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral…
The Thue-Siegel method is used to obtain an upper bound for the number of primitive integral solutions to a family of quartic Thue's inequalities. This will provide an upper bound for the number of integer points on a family of elliptic…
We study the spherical slice transform which assigns to a function on the $n$-dimensional unit sphere the integrals of that function over cross-sections of the sphere by $k$-dimensional affine planes passing through the north pole. These…
In this note we study numerically the combinatorics of curves and geodesics on the torus with one boundary component. A potential computational difficulty is avoided by counting inside specific orbits of the mapping class group up to a…
Photometric data from the literature is combined with triaxial mass models to derive variation in the intrinsic shapes of the light distribution of elliptical galaxies NGC 720, 2768 and 3605. The inferred shape variation in given by a…
In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that…
Real and imaginary part of the limit 2N->infinity of the integral int_{x=1..2N} exp(i*pi*x)*x^(1/x) dx are evaluated to 20 digits with brute force methods after multiple partial integration, or combining a standard Simpson integration over…
In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not…
Estimates for elliptic flow in collisions of polarized light nuclei with spin $j\ge1$ with a heavy nucleus are presented. In such collisions the azimuthal symmetry is broken via polarization of the wave function of the light nucleus,…
Let \( E \) be a complex elliptic curve with conductor \( N \) and modular invariant \( j(E) \in \mathbb{Q} \). We construct a class of modular polynomials $F_N(x,j)$ that relate the modular function $x$ on $X_0(N)$ to the $j$-invariant…
The paper is devoted to the study of graph sequence G_n = (V_n, E_n) where V_n is the set of all vectors v in R^n with coordinates from {-1, 0, 1} such that |v| = sqrt(3), and E_n consists of all pairs of vertices with the scalar product 1.…
Every Euclidean domain $R$ has a minimal Euclidean function, $\phi_R$. A companion paper \cite{Graves} introduced a formula to compute $\phi_{\mathbb{Z}[i]}$. It is the first formula for a minimal Euclidean function for the ring of integers…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
We consider embedded ring-type surfaces (that is, compact, connected, orientable surfaces with two boundary components and Euler-Poincar\'{e} characteristic zero) in ${\bold R}^3$ of constant mean curvature which meet planes $\Pi_1$ and…
We study integro-differential elliptic equations (of order $2s$) with variable coefficients, and prove the natural and most general Schauder-type estimates that can hold in this setting, both in divergence and non-divergence form.…