1,332 research outputs found
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
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