Related papers: A root elliptic function in signature four

We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study their properties through the use of descent functions.…

We consider a rational elliptic surface with a relatively minimal fibration. We compute the number of integral sections in the above rational elliptic surface. As an application, we obtain an estimate of polynomial solutions of some…

In this short, we study sums of the shape $\sum_{n\leqslant x}{f([x/n])}/{[x/n]},$ where $f$ is Euler totient function $\varphi$, Dedekind function $\Psi$, sum-of-divisors function $\sigma$ or the alternating sum-of-divisors function…

In this note we review some results regarding higher order elliptic differential operators on manifolds without boundary.

We give a new perspective on the Lorentzian OPE inversion formula of arXiv:1703.00278, building on arXiv:2302.06469. We introduce an ``auxiliary'' fourpoint function that can be related to the traditionally defined ones via a Radon…

The second derivative of a function r(t) with respect to a variable t is equal to -n times the function raised to the 2n-1 power of r(t); using this definition, an ordinary differential equation is constructed. Graphs with the horizontal…

In this paper we prescribe a fourth order conformal invariant on the standard $n-$sphere, with $n\geq5$, and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up…

We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These…

In the study of holomorphic functions of one complex variable, one well-known theory is that of elliptic functions and it is possible to take the zeta-function of Weierstrass as a building stone of this vast theory. We are working the…

Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an elipsoid using…

We introduce a new method of symmetrization of mappings on the $n$-sphere ($n\geq 2$). They are applied to estimate solutions of quasilinear elliptic partial differential equations of $p$-Laplacian type, with combinations of Dirac measures…

We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…

We show that every member of an infinite family of symplectic manifolds constructed by R. Inanc Baykur, Kenta Hayano, and Naoyuki Monden (arXiv:1903:02906) is diffeomorphic to an elliptic surface. As a result: (1) the symplectic Calabi-Yau…

We study elliptic functions in quaternionic analysis, and prove some analogues of classical theorems from the complex case. The main result is a relation between the periods of closed differential 1-forms and 3-forms on H/L where L is a…

We give a new proof of Chen-Lin result with Li-Zhang method.

Recently, Hong, Mertens, Ono and Zhang proved a conjecture of C\u{a}ld\u{a}raru, He, and Huang that expresses the Taylor series of the modular $j$-function around the elliptic points $i$ and $\rho=e^{\pi i/3}$ as rational functions arising…

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean…

In this article we present evaluations of continued fractions studied by Ramanujan. More precisely we give the complete polynomial equations of Rogers-Ramanujan and other continued fractions, using tools from the elementary theory of the…

We investigate the elliptic integrable model introduced by Deguchi and Martin, which is an elliptic extension of the Perk-Schultz model. We introduce and study a class of partition functions of the elliptic model by using the…

In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator…