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Twisted Weyl Group Multiple Dirichlet Series: The Stable Case
Stable Case Multiple Dirichlet Series
2015/7/6
Weyl group multiple Dirichlet series were associated with a root system Φ and a number
field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] an...
Given a root system Φ of rank r and a global field F containing the n-th
roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose
coefficients are n-th ...
Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory
Type A Combinatorial Theory Dirichlet Series
2015/7/6
Speci cally, two distinct versions of the Gelfand-Tsetlin de nition were given. It
is not apparent that they are equal. Either of these de nitions is purely local in that
it speci es the p-part of t...
Weyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
Eisenstein Series Crystal Bases
2015/7/6
If F is a local eld containing the group n of n-th roots of unity, and if G is a split
semisimple simply connected algebraic group, then Matsumoto [27] de ned an n-fold
covering group of G(F), tha...
Coefficients of the n-fold Theta Function and Weyl Group Multiple Dirichlet Series
Dirichlet Series Theta Function
2015/7/6
We establish a link between certain Whittaker coecients of the generalized
metaplectic theta functions, rst studied by Kazhdan and Patterson [14], and
the coecients of the stable Weyl group multi...
This introductory article aims to provide a roadmap to many of the
interrelated papers in this volume and to a portion of the field of multiple Dirichlet
series, particularly emerging new idea...
WEYL GROUP MULTIPLE DIRICHLET SERIES OF TYPE A2
Dirichlet series rational function gaussian type
2014/12/25
A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system . The number of variables equals the rank r of the root system, and the series sati...
Weyl group multiple Dirichlet series constructed from quadratic characters
Dirichlet coefficient function equation of variable properties
2014/12/25
We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain gr...
On the p-parts of quadratic Weyl group multiple Dirichlet series
Reduce the root dirichlet level dirichlet series
2014/12/24
Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1,…, sr , initially converging for (si) sufficiently large, which h...
LITTELMANN PATTERNS AND WEYL GROUP MULTIPLE DIRICHLET SERIES OF TYPE D
Vail group the root type pattern
2014/12/24
We formulate a conjecture for the local parts of Weyl group multiple Dirichlet series attached to root systems of type D. Our conjecture is analogous to the description of the local parts of type A se...
CONSTRUCTING WEYL GROUP MULTIPLE DIRICHLET SERIES
Lower level dirichlet series gathered themselves together transformation
2014/12/24
Let be a reduced root system of rank . A Weyl group multiple Dirichlet series for is a Dirichlet series in complex variables , initially converging for sufficiently large, that has meromorphic continu...
Twisted Weyl Group Multiple Dirichlet Series Over the Rational Function Field
Rational Function Field Multiple Dirichlet
2014/12/8
Let K be a global field. For each prime p of K, the p-part of a multiple Dirichlet series defined over K is a generating function in several variables for the p-power coefficients. Let _ be an irreduc...
An Elliptic Analogue Of Generalized Cotangent Dirichlet Series And Its Transformation Formulae At Some Integer Arguments
Elliptic Analogue Cotangent Dirichlet Series Integer Arguments Number Theory
2011/9/20
Abstract: B.C. Berndt evaluated special values of the cotangent Dirichlet series. T. Arakawa studied a generalization of the series, or generalized cotangent Dirichlet series, and gave its transformat...
The generating function for the Dirichlet series Lm(s)
Dirichlet series generalized Euler and class number ∧-alternating augmented m-signed permutation r-cubical lattice Springer number
2014/6/3
The Dirichlet series Lm(s) are of fundamental importance in number theory. Shanks defined the generalized Euler and class numbers in connection with the Dirichlet series, denoted by {sm, n}n≥0. We obt...
Local properties of Hilbert spaces of Dirichlet series
Local properties Hilbert spaces Dirichlet series
2010/11/19
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This ex...