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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...
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...
Extending Landau's Theorem on Dirichlet Series with Non-Negative Coefficients
Extending Landau's Theorem Non-Negative Coefficients
2010/11/26
A classical theorem of Landau states that, if an ordinary Dirichlet series has non-negative coefficients, then it has a singularity on the real line at its abscissae of absolute convergence.
Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two
Dirichlet Series Attached Siegel Modular Forms Degree Two
2010/12/8
The Rankin convolution type Dirichlet series DF,G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G.
On the Distribution of Random Dirichlet Series in the Whole Plane
Random Dirichlet series Order(R) strong Borel line little function
2010/2/25
For some random Dirichlet series of order(R) infinite almost surely, every horizontal line is a strong Borel line of order(R) infinite and without exceptional Little functions.
The significance of the comultiplication is that it determines a
multiplicative structure on the tensor category of representations.
ON SPACES OF GENERALIZED DIRICHLET SERIES
GENERALIZED DIRICHLET SERIES space A1(\bar{A} spaces Lf(l,s)
2010/3/17
It is considered the relationship between spaces Lf(l,s) and subspaces of the space A1(\bar{A}1) of analytic functions in the open (closed) unit disc, generated by systems F(anz), n\in N, if they cons...