We obtain a 3-fold Selberg integral formula. As a consequence we are able to compute the explicit value of the sharp constant in a trilinear fractional integral inequality due to Beckner.

We develop algorithms for computations of Green’s function and its Fourier coefficients, Fn(z; s), on Fuchsian groups with one cusp. An analog of a Rankin-Selberg bound for Fn(z; s) is presented.

Let $\varrho$ be a complex number and let $f$ multiplicative arithmetic function whose Dirichlet series takes the form $\zeta(s)^\varrho G(s)$, where $G$ is associated to $g$. The classical Selberg-Delange method furnishes asymptotic estimates for averages of under assumptions either analytic continuation $G$, or absolute convergence finite derivatives $G(s)$ at $s=1$. We consider different set...

Dynamical zeta functions [1], Fredholm determinants [2] and quantum Selberg zeta functions [3, 4] have recently been established as powerful tools for evaluation of classical and quantum averages in low dimensional chaotic dynamical systems [5] [8]. The convergence of cycle expansions [9] of zeta functions and Fredholm determinants depends on their analytic properties; particularly strong resul...

1. The trace formula of Selberg reduces the problem of calculating the dimension of a space of automorphic forms, at least when there is a compact fundamental domain, to the evaluation of certain integrals. Some of these integrals have been evaluated by Selberg. An apparently different class of definite integrals has occurred in Harish-Chandra’s investigations of the representations of semi-sim...