相关论文: Elliptic Selberg integrals

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.

We give a sup $\times$ inf inequality for an elliptic equation.

A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.

The table of Gradshteyn and Ryzhik contains many entries that are related to elliptic integrals. We present a systematic derivation of some of them.

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

We give an index formula for elliptic differential operators whose coefficients include shifts forming an infinite group.

We prove a duality formula between two elliptic determinants. We present a proof which is a variant of the Izergin-Korepin method which is a method originally introduced to analyze and compute partition functions of integrable lattice…

We prove a two-dimensional $\mathbb F_p$-Selberg integral formula, in which the two-dimensional $\mathbb F_p$-Selberg integral $\bar S(a,b,c;l_1,l_2)$ depends on positive integer parameters $a,b,c$, $l_1,l_2$ and is an element of the finite…

In this paper, we consider a discrete version of iterated integrals by the naive (equally divided) Riemann sum. In particular, basic three formulas for usual iterated integrals are discritized. Moreover, we proved cyclic sum formulas for…

We prove the universality theorem for the iterated integrals of logarithms of $L$-functions in the Selberg class on some line parallel to the real axis.

We prove a generalization of the $q$-Selberg integral evaluation formula. The integrand is that of $q$-Selberg integral multiplied by a factor of the same form with respect to part of the variables. The proof relies on the quadratic norm…

We use some general properties, presented in previous work, to evaluate special cases of integrals relating Rogers-Ramanujan continued fraction, eta function and elliptic integrals.

In this article I will review some basic results on elliptic boundary value problems with applications to General Relativity.

We propose in this paper to study the solutions of some nonlinear elliptic equations with singular potential.

We provide the explicit formula for orbital integrals associated with elliptic regular semisimple elements in $\mathrm{GL}_n(F) \cap \mathrm{M}_n(\mathfrak{o})$ and associated with arbitrary elements of the spherical Hecke algebra of…

The article provides the formula for the calculation the falling time of inverted pendulum. The result is expressed in terms of elliptic integrals of first kind. The asymptotic formula for small initial inclination value is also provided.

Let $P$ be an arbitrary point on an elliptic curve over the complex numbers of the form $y^2=x^3+a_4\,x+a_6$ or of the form $y^2=x^3+a_2\,x^2+a_4\,x$. We provide explicit formulae to compute the points $P/2$, i.e., the points $Q$ such that…

The evaluation formula for an elliptic beta integral of type $G_2$ is proved. The integral is expressed by a product of Ruijsenaars' elliptic gamma functions, and the formula includes that of Gustafson's $q$-beta integral of type $G_2$ as a…

We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.

We propose three kinds of explicit formulas for the elliptic lambda function by the elliptic modular function. Further, we derive incredible cubic identities as a corollary of our explicit formulas and evaluate some singular values of the…