Related papers: Selberg Integrals

This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].

We study the arithmetic (real) function f=g*1, with g "essentially bounded" and supported over the integers of [1,Q]. In particular, we obtain non-trivial bounds, through f "correlations", for the "Selberg integral" and the "symmetry…

In this paper we obtain new theorems about classes of exceptional sets for the Selberg's theorem C (1942). Our theorems, as based on discrete method, are not accessible for Karatsuba's theory (1984) since this theory is a continuous theory.…

The purpose of this book is to provide an introduction to one of the fundamental tools of abstract harmonic analysis, namely the Selberg trace formula.

This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.

Analytic expressions for integrals which arise in a theory of atomic structure due to Schwinger and Englert are evaluated in terms of Bessel and Struve functions

In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.

Written for the book "Mathematicians from Saint Petersburg and their theorems".

This is an expanded version of the author's lecture at the XX Congresso U.M.I., held in Siena in September 2015. After a brief review of L-functions, we turn to the classical converse theorems of H.Hamburger, E.Hecke and A.Weil, and to some…

We translate the paper De Integralibus quibusdam definitis, seriebusque infinitis

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral…

These notes contain a revisit to the matrix construction of the Weil representation by the author in the Journal of Algebra in 1972.

This article has a twofold purpose. On the one hand I would like to draw attention to some nice exercises on the Kepler laws, due to Otto Laporte from 1970. Our discussion here has a more geometric flavour than the original analytic…

In this revised version, we add some expository material and references and make some minor corrections.

We give an alternative proof of the evaluation formula for the elliptic Selberg integral of type $BC_n$ as an application of the fundamental $BC_n$-invariants.

The paper concerns singular solutions of nonlinear elliptic equations.

Final version, to appear in Mathematical Research Letters.

This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006) and follows its referencing guidelines.

Submitted to F. Schweitzer (ed.), Microscopic Models for Economic Dynamics, Lecture notes in physics, Springer, Berlin-Heidelberg 2002.kiel.tex

I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.