Related papers: Elliptic Selberg integrals
An elliptic analogue of the $q$ deformed Knizhnik-Zamolodchikov equations is introduced. A solution is given in the form of a Jackson-type integral of Bethe vectors of the XYZ-type spin chains.
A generalization of Selberg's beta integral involving Schur polynomials associated with partitions with entries not greater than 2 is explicitly computed. The complex version of this integral is given after proving a general statement…
We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.
In this work we construct logarithms and Birkhoff normal forms for elliptic Fourier integral operators in the semi-classical limit under more general assumptions than in aprevious work by the first author. The methods are similar but…
Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson,…
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
We provide a new characterization of the logarithmic Sobolev inequality.
We derive special forms of the Poisson summation formula for even and odd functions, which are applied to obtain representations for Euler-type numbers and to sum various series related to elliptic functions.
We give the rate of convergence of some optimal lower Riemann-Stieltjes sums toward the integral.
We derive new integral representations for objects arising in the classical theory of elliptic functions: the Eisenstein series $E_s$, and Weierstrass' $\wp$ and $\zeta$ functions. The derivations proceed from the Laplace-Mellin…
We obtain an explicit integral representation of Siegel-Whittaker functions on Sp(2,R) for the large discrete series representations. We have another integral expression different from that of Miyazaki [7].
We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.
Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in in 1940s. The original versions of these sums were introduced by R.J.Evans in 1981 and, following an elegant idea of G.W.Anderson in 1991 they were…
In this work we prove the existence of a classical positive solution for an elliptic equation with a sublinear term. We use Galerkin approximations to show existence of such solution on bounded domains in RN.
The spinless Salpeter equation presents a rather particular differential operator. In this paper we rewrite this equation into integral and integro-differential equations. This kind of equations are well known and can be more easily…
We propose a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal) operators associated with regular Dirichlet forms and with measure data. Using the theory of backward stochastic differential…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
We describe iterated integrals as unipotent periods on families of marked elliptic curves in terms of multiple zeta values and elliptic multiple zeta values.
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.
The weighted Selberg integral is a discrete mean-square, that is a generalization of the classical Selberg integral of primes to an arithmetic function $f$, whose values in a short interval are suitably attached to a weight function. We…