Some integration formulas which either occur or are implicit in Ha’s recent exact calculation of some correlations in the Calogero-Sutherland model are discussed. These integration formulas include the calculation of the inner product < 0|ρ(0)|κ > between the density operator acting on an excited state and the ground state, and a generalization of the Selberg integral due to Dotsenko and Fateev.

We give the (Ahumada type) Selberg trace formula for a semiregular bipartite graph G: Furthermore, we discuss the distribution on arguments of poles of zeta functions of semiregular bipartite graphs. As an application, we present two analogs of the semicircle law for the distribution of eigenvalues of specified regular subgraphs of semiregular bipartite graphs. r 2003 Elsevier Science (USA). Al...

For Kleinian groups acting on hyperbolic three-space, we prove factorization formulas for both the Selberg zeta-function and the automorphic scattering matrix. We extend results of Venkov and Zograf from Fuchsian groups, to Kleinian groups, and we give a proof that is simple and extendable to more general groups.

Based on the ideas in some recently uncovered notes of Selberg [14] on discrete subgroups of a product of SL2(R)’s, we show that a discrete subgroup of SL3(R) generated by lattices in upper and lower triangular subgroups is an arithmetic subgroup and hence a lattice in SL3(R).

In this paper we construct a Rankin-Selberg integral which represents the Spin10× St L-function attached to the groupGSO10×PGL2. We use this integral representation to give some equivalent conditions for a generic cuspidal representation on GSO10 to be a functorial lift from the group G2 × PGL2.

The discrete decomposition with finite multiplicities of square-integrable cuspforms, and concommitant estimates, are foundational. Lie-group and symmetric-space versions of these results were known [Selberg 1956], [Gelfand-Fomin 1952] in the mid 1950’s. The general assertion was made in [GelfandGraev 1962] and [Gelfand-PS 1963], the latter observing that an adelic formulation can proceed in th...

Let C ′ ⊂ √ 2 be arbitrary. In [15], the main result was the derivation of singular, continuously nonnegative isomorphisms. We show that every linearly left-Erdős functor is pseudo-totally nonn-dimensional and algebraically null. D. Li [15, 15] improved upon the results of L. Pythagoras by studying Selberg scalars. In [14], the authors examined algebraic hulls.

We study the twisted homology group attached to a Selberg type integral under some resonance condition, which naturally appears in the su2conformal field theory and the representation of the Iwahori-Hecke algebra. We determine the dimension of the space of the regularizable cycles. The dimensionformula is given in terms of the generalized hypergeometric series 3F2.

1. Harmonic analysis on H 2. Meromorphic continuation up to the critical line 3. Sobolev inequality/imbedding 4. Eventually-vanishing constant terms 5. Compactness of Sob(Γ\H)a → L(Γ\H) 6. Discreteness of cuspforms 7. Meromorphic continuation beyond the critical line 8. Discrete decomposition of truncated Eisenstein series 9. Appendix: Friedrichs extensions 10. Appendix: simplest Maass-Selberg ...

In this paper we calculate the asymptotics of various moments of the central values of Rankin-Selberg convolution L-functions of large level, thus generalizing the results and methods of W. Duke, J. Friedlander, and H. Iwaniec and of the authors. Consequences include convexity-breaking bounds, nonvanishing of a positive proportion of central values, and linear independence results for certain H...