相关论文: Elliptic Selberg integrals
In this paper we study the existence of solutions of thedegererate elliptic system.
In this paper, we prove some isoperimetric inequalities and give a sharp bound for the positive solution of sublinear elliptic equations.
In this paper the authors investigate a power mean inequality for a special function which is defined by the complete elliptic integrals.
It is shown how to define difference equations on particular lattices $\{x_n\}$, $n\in\mathbb{Z}$, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special…
In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are…
This paper will be replaced later by a revised version.
We show how to efficiently compute Hilbert modular forms as orthogonal modular forms, generalizing and expanding upon the method of Birch.
The complete $p$-elliptic integrals are generalizations of the complete elliptic integrals by the generalized trigonometric function $\sin_p{\theta}$ and its half-period $\pi_p$. It is shown, only for $p=4$, that the generalized…
We describe a method to compute Hurwitz-Hodge integrals.
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…
This paper presents the basic ideas and properties of elliptic functions and elliptic integrals as an expository essay. It explores some of their numerous consequences and includes applications to some problems such as the simple pendulum,…
We give a brief review of the main results of the theory of elliptic hypergeometric functions -- a new class of special functions of mathematical physics. We prove the most general univariate exact integration formula generalizing Euler's…
We derive level set version of partial uniform ellipticity for symmetric concave functions. This suggests an effective approach to investigate second order fully nonlinear equations of elliptic and parabolic type.
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…
Some identities that involve the elliptic version of the Cauchy matrices are presented and proved. They include the determinant formula, the formula for the inverse matrix, the matrix product identity and the factorization formula.
We derive a local uniform boundedness result for an elliptic equation having interior singularity.
In this paper, we find a new recurrence formula fo the Euler zeta functions.
We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effective method for computing Weierstrass functions, their…
The complete elliptic integrals are generalized by using the generalized trigonometric functions with two parameters. It is shown that a particular relation holds for the generalized integrals. Moreover, as an application of the integrals,…
This paper gives a fairly explicit formula for the Hilbert series of algebras of Veronese type.