We present a generalisation of the famous Selberg integral. This confirms the g = An case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for each simple Lie algebra g. Résumé. On présente une généralisation de la bien connue intégrale de Selberg. Cette généralisation vérifie le cas g = An de la conjecture de Mukhin et Varchenko concernant l’existence d’un...

In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.

Abstract Let F be a totally real field, and let $E/F$ CM quadratic extension. We construct p -adic L -function attached to Hida families for the group $\mathrm {GL}_{2/F}\times \mathrm {Res}_{E/F}\mathrm {GL}_{1}$ . It is characterized by an exact interpolation property critical Rankin–Selberg -values, at classical points corresponding representations $\pi \boxtimes \chi $ with weights of $\chi...

We prove that certain screening operators in conformal field theory obey the algebra relations of a corresponding Nichols with diagonal braiding. Our result proves particular long-standing expectation Borel parts small quantum groups appear as operators. The proof is based on novel, intimate relation between Hopf algebras, vertex algebras and class multivalued analytic special functions, which ...

Let F be a number field, G the general linear group of degree n defined over F. Let π be an irreducible cuspidal automorphic representation of G(A). In [1–3], a Rankin-Selbergtype integral is constructed to represent the L function of π. That the integrals of Jacquet, Piatetski-Shapiro, and Shalika are Eulerian follows from the uniqueness of Whittaker models and the fact that cuspidal represent...

We prove the properties of induced conjugacy classes, without using the original proof by Lusztig and Spaltenstein in the unipotent case, by adapting Borho’s simpler arguments for induced adjoint orbits. We study properties of equivariant fibrations of prehomogeneous affine spaces, especially the existence of relative invariants. We also detect prehomogeneous affine spaces as subquotients of ca...

We prove an $\mathbb F_p$-Selberg integral formula of type $A_n$, in which the is element finite field F_p$ with odd prime number $p$ elements. The motivated by analogy between multidimensional hypergeometric solutions KZ equations and polynomial same reduced modulo $p$. For $A_1$ was proved a previous paper authors.

in this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by boundary elements. the integrals in boundary integrals equations are inherently singular. for example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

A new family of probability distributions βM,N , M = 0 · · ·N, N ∈ N on the unit interval (0, 1] is defined by the Mellin transform. The Mellin transform of βM,N is characterized in terms of products of ratios of Barnes multiple gamma functions, shown to satisfy a functional equation, and a Shintani-type infinite product factorization. The distribution log βM,N is infinitely divisible. If M < N...