Weyl group multiple Dirichlet series II: The stable case

To each reduced root system Φ of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r complex variables, whose group of functional equations is isomorphic to the Weyl group of Φ. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, the number of nonzero such coefficients is equal to the order of the Weyl group, and each nonzero coefficient is a product of n-th order Gauss sums. The root system plays a basic role in the combinatorics underlying the proof of the functional equations.     

On the dimension of the space of theta functions

We compute the dimension of the space of theta functions of a given type using a variant of the Selberg trace formula.

     

Spin L-functions on

The ``spin' L-function of an automorphic representation of is an Euler product of degree associated with the spin representation of the L-group . If or , and the automorphic representation is generic in the sense of having a Whittaker model, the analytic properties of these L-functions are studied by the Rankin-Selberg method.

     

An L-Function of Degree 27 for Spin9

This paper studies a Rankin-Selberg integral for a degree 27 L-function on Spin(9). It makes use of an Eisenstein series on the exceptional group F ₄.     

Iron-plasma transmission measurements at temperatures above 150 eV

Measurements of iron-plasma transmission at 156+/-6 eV electron temperature and 6.9+/-1.7 x 10(21) cm(-3) electron density are reported over the 800-1800 eV photon energy range. The temperature is more than twice that in prior experiments, permitting the first direct experimental tests of absorption features critical for understanding solar interior radiation transport. Detailed line-by-line opacity models are in excellent agreement with the data.     

Whittaker–Fourier Coefficients of Metaplectic Eisenstein Series

It is shown that the Fourier–Whittaker coefficients of Eisenstein series on the n-fold cover of GL(n) are L-functions, improving prior results of T. Suzuki.     

On the Averages of Characteristic Polynomials From Classical Groups

We provide an elementary and self-contained derivation of formulae for averages of products and ratios of characteristic polynomials of random matrices from classical groups using classical results due to Weyl and Littlewood. The first author was supported in part by the NSF grant FRG DMS-0354662. The second author was supported in part by the NSF postdoctoral fellowship and by the NSF grant DMS-0501245.