We develop a partial trace formula which circumvents some technical difficulties in computing the Selberg trace formula for the quotient SL3(Z)\SL3(R)/SO3(R). As applications, we establish the Weyl asymptotic law for the discrete Laplace spectrum and prove that almost all of its cusp forms are tempered at infinity. The technique shows there are non-lifted cusp forms on SL3(Z)\SL3(R)/SO3(R) as w...

The convergence properties of cycle expanded periodic orbit expressions for the spectra of classical and semiclassical time evolution operators have been studied for the open three disk billiard. We present evidence that both the classical and the semiclassical Selberg zeta function have poles. Applying a Padé approximation on the expansions of the full Euler products, as well as on the individ...

5 Introduction In 1956 A. Selberg introduced the zeta function Z(s) = c N ≥0 (1 − e −(s+N)l(c)), Re(s) >> 0, where the first product is taken over all primitive closed geodesics in a compact Riemannian surface of genus ≥ 2, equipped with the hyperbolic metric, and l(c) denotes the length of the geodesic c. Selberg proved that the product converges if the real part of s is large enough and that ...

In their 2011 paper on the AGT conjecture, Alba, Fateev, Litvinov and Tarnopolsky (AFLT) obtained a closed-form evaluation for Selberg integral over product of two Jack polynomials, thereby unifying well-known Kadell Hua--Kadell integrals. this we use variety symmetric functions function techniques to prove generalisations AFLT integral. These include (i) an $\mathrm{A}_n$ analogue integral, co...

Recension av: Historien in på livet. Diskussioner om kulturarv och minnespolitik. Red. Anne Eriksen, Jan Garnert Torunn Selberg. Falun 2002. 277 s.

In this note we present a polynomial bound on the distribution of poles of the scattering operator for the Laplacian on certain hyperbolic manifolds M of infinite volume. The motivation is to understand more fully the geometry of the poles of the scattering operator. The proof uses the relationship between poles of the scattering operator and zeros of the Selberg zeta function for geodesic flow...

In this article, we study p-adic torus periods for certain p-adic valued functions on Shimura curves coming from classical origin. We prove a p-adic Waldspurger formula for these periods, as a generalization of the recent work of Bertolini, Darmon, and Prasanna. In pursuing such a formula, we construct a new anti-cyclotomic p-adic L-function of Rankin– Selberg type. At a character of positive w...

By employing a method of parameterizations for Ramanujan's theta-functions, we find several modular relations and explicit values of the Ramanujan-Selberg continued fractions .

It is proved that under some suitable conditions, the degree two functions in the Selberg class have infinitely many zeros on the critical line.