Weyl group multiple Dirichlet series of type A_2

A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Phi. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of Phi. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n-th order Gauss sums attached to the root system of type A_2. The basic technique is to construct a rational function in r variables invariant under a certain action of W, and use this to build a ``local factor'' of the global series

On Iwahori-Whittaker Functions for Metaplectic Groups

We relate Iwahori-Whittaker functions on metaplectic covers to certain Demazure-Lusztig operators, the latter of which are built from a Weyl group action previously considered by G. Chinta and P. Gunnells. Using a certain combinatorial identity for the sum of these Demazure-Lusztig operators, we obtain an analogue of the Casselman-Shalika formula for spherical Whittaker functions in this context.Comment: Previous version had title "On the Casselman-Shalika formula for metaplectic groups

Comparing Health Care Systems in Canada/UK, USA and Switzerland to Assess the Direction of US Health Care Reform

Along the payer continuum ranging from fullconsolidation of payers to consumer-driven health care,three competing models of health care systems areidentified in Canada/UK, USA and Switzerlandrespectively. These three health care systems arecompared and contrasted along 10 analyticaldimensions. Trade-offs along three aspects of a healthcare system, namely, (i) access to care, (ii) quality ofcare, and (iii) cost of care, are discussed in each of thethree systems. Bureaucratic forces in Canada/UK,competitive forces in USA and market forces inSwitzerland are noted as dominant. Several state-levelmini-reforms in the USA are noted with a view toproject the direction of future of US health care system.The paper concludes with an inferential projection oftransforming forces impinging on the current US healthcare system

Complexity and heights of tori

We prove detailed asymptotics for the number of spanning trees, called complexity, for a general class of discrete tori as the parameters tend to infinity. The proof uses in particular certain ideas and techniques from an earlier paper. Our asymptotic formula provides a link between the complexity of these graphs and the height of associated real tori, and allows us to deduce some corollaries on the complexity thanks to certain results from analytic number theory. In this way we obtain a conjectural relationship between complexity and regular sphere packings.Comment: 14 page

Noncommutative modular symbols and Eisenstein series

We form real-analytic Eisenstein series twisted by Manin's noncommutative modular symbols. After developing their basic properties, these series are shown to have meromorphic continuations to the entire complex plane and satisfy functional equations in some cases. This theory neatly contains and generalizes earlier work in the literature on the properties of Eisenstein series twisted by classical modular symbols.Comment: 19 pages, minor corrections and added references. To appear in the conference proceedings of Building Bridges