Related papers: Selberg Integrals
We use the elliptic interpolation kernel due to the second author to prove an $\mathrm{A}_n$ extension of the elliptic Selberg integral. More generally, we obtain elliptic analogues of the $\mathrm{A}_n$ Kadell, Hua-Kadell and…
Using an extension of the well-known evaluation symmetry, a new Cauchy-type identity for Macdonald polynomials is proved. After taking the classical limit this yields a new sl_3 generalisation of the famous Selberg integral. Closely related…
We reduce some key calculations of compositions of morphisms between Soergel bimodules ("Soergel calculus") to calculations in the nil Hecke ring ("Schubert calculus"). This formula has several applications in modular representation theory.
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
We study a new Selberg-type integral with $n+m$ indeterminates, which turns out to be related to the deformed Calogero-Sutherland systems. We show that the integral satisfies a holonomic system of $n+m$ non-symmetric linear partial…
We obtain an explicit formula for a certain weighted enumeration of lozenge tilings of a hexagon with an arbitrary triangular hole. The complexity of our expression depends on the distance from the hole to the center of the hexagon. This…
This article surveys the Euler calculus - an integral calculus based on Euler characteristic - and its applications to data, sensing, networks, and imaging.
To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.
This is a copy of the article published in Math Res. Letters 5, (1998) 497-516.
In this article we consider the elliptic Selberg integral, which is a BC_n symmetric multivariate extension of the elliptic beta integral. We categorize the limits that are obtained as p->0, for given behavior of the parameters as p->0.…
This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.
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…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
We present a summary of recent and older results on Bessel integrals and their relation with zeta numbers.
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…
This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006).
This is an English translation of the monograph "Die Klassenk\"orper der komplexen Multiplikation" by Max Deuring, published in 1958 as Enzyklop\"adie der Mathematischen Wissenschaften, Band I-2, Heft 10, Teil II by B.G. Teuber…
We analyze the situation which is related to zonal spherical functions of type $A_n$ and obtain a generalization of Selberg integral.
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…
Some new integrals involving the Stieltjes constants are developed in this paper.