相关论文: Elliptic Selberg integrals
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.
A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previously known results. These formulas provide a well-defined algorithm for computing Selberg-Schur…
We survey on algebraically elliptic varieties in the sense of Gromov.
We prove an $\mathbb F_p$-Selberg integral formula, in which the $\mathbb F_p$-Selberg integral is an element of the finite field $\mathbb F_p$ with odd prime number $p$ of elements. The formula is motivated by analogy between…
We give a new non-trivial upper bound for the Selberg integral of the three-divisor function $d_3(n)$. Our method applies our recent conjecture together with Laporta, for the modified Selberg integral of $d_3(n)$, and a kind of modified…
We discuss some aspects of the theory of subelliptic estimates.
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
We show how to determine the asymptotics of a certain Selberg-type integral by means of tools available in the theory of (generalised) hypergeometric series. This provides an alternative derivation of a result of Carr\'e, Deneufch\^atel,…
In this note we give a closed formula for Faltings' delta-invariant of a hyperelliptic Riemann surface.
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
We present the moste recent results dealing with the theory of semilinear elliptic equations with measures data
We prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems. Using the (A,C) inversion formula to invert one of the known C-type elliptic beta integrals, we obtain a new elliptic…
In this paper, we show that the coefficient of the Taylor expansion of Selberg integrals with respect to exponent variables are expressed as a linear combination of multiple zeta values. We use beta-nbc base so that the Selberg integral is…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
We introduce and prove evaluations for families of multiple elliptic integrals by solving special types of ordinary and partial differential equations. As an application, we obtain new expressions of Ramanujan-type series of level 4 and…
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel…
In this article we prove a new elliptic hypergeometric integral identity. It previously appeared (as a conjecture) in articles by Rains, and Spiridonov and Vartanov. Moreover it gives a different proof of an identity in another article by…
A class of log-trigonometric integrals are evaluated in terms of elliptic functions. From this, by using the elliptic integral singular values, one can obtain closed form evaluations of integrals such as \[…
Several methods of evaluation are presented for a family of Selberg-like integrals that arose in the computation of the algebraic-geometric degrees of a family of multiplicity-free nilpotent K_C-orbits. First, adapting the technique of…
A simple integral formula as an iterated residue is presented for the Baker-Akhiezer function related to $A_n$ type root system both in the rational and trigonometric cases. We present also a formula for the Baker-Akhiezer function as a…