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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 ...
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...
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...
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...
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...
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 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...
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...
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.
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.
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.
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...

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