相关论文: Selberg Integrals
Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM
Selberg introduced his beautiful integral formula in 1944, see [Sel]. Evans [E1] conjectured a finite field analog of Selberg integral formula in 1980. And Anderson [An] proved a major case of it in 1981 and his ideas was used to obtained…
This document describes the authors' current research project: the evaluation of a tower of Rankin-Selberg integrals on the group E_6. We recall the notion of a tower, and two known towers, making observations about how the integrals within…
This paper has been withdrawn due to an error, and no further revisions will be made.
This is an English translation of Felix Klein's paper "Ueber die Transformation elfter Ordnung der elliptischen Functionen" from 1879.
It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…
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…
Short review article on quantum information processing accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM
Some personal thoughts on Sklar's theorem and copulas after reading the original paper (Sklar, 1959) in French.
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
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…
The Selberg correlation integrals are averages of the products $\prod_{s=1}^m\prod_{l=1}^n (x_s - z_l)^{\mu_s}$ with respect to the Selberg density. Our interest is in the case $m=1$, $\mu_1 = \mu$, when this corresponds to the $\mu$-th…
This is the original paper appeared in the book "Elliptic and Parabolic Methods in Geometry (Minneapolis, MN,1994), A K Peters, Wellesley, MA, (1996)" (p.1-16), except with a few minor modifications as described at the end of the paper (on…
The work studies some Difference equations, which are connected with Mejer's function.
The paper suggests a slightly more rigorous justification to Wang et al.'s work from 2007, and introduces the Slanted Line Integral.
This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.
A translation of Kummer`s paper On certain definite integrals and infinite series
Draft version of an article prepared for the Encyclopedia of Mathematical Physics, Elsevier, to appear in 2006.
In this paper we present a combinatorial proof of Selberg's integral formula. We start by giving a bijective proof of a Theorem about the number of topological orders of a certain related directed graph. Selberg's Integral Formula then…
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.