Results 1 to 10 of about 114,475 (241)
Weyl group multiple Dirichlet series constructed from quadratic characters [PDF]
Inventiones Mathematicae, 2006 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 group of functional equations.
A. Diaconu +16 more
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Journal of Number Theory, 2000 A sequence \(\{u_n\}_{n\geq 0}\) is \(d\)-automatic if its \(n\)-th term can be computed by a finite-state machine using the base \(d\) expansion of the integer \(n\). To such a sequence corresponds a sequence of \(t\)-dimensional vectors \(\{U_n\}_{n\geq 0}\), whose first components give the sequence \(\{u_n\}_{n\geq 0}\), and \(d\) matrices \(A_0,A_1,
Allouche, J.-P +2 more
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Fréchet spaces of general Dirichlet series [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 Inspired by a recent article on Fr chet spaces of ordinary Dirichlet series $\sum a_n n^{-s}$ due to J.~Bonet, we study topological and geometrical properties of certain scales of Fr chet spaces of general Dirichlet spaces $\sum a_n e^{- _n s}$. More precisely, fixing a frequency $ = ( _n)$, we focus on the Fr chet space of $ $-Dirichlet series ...
Andreas Defant +3 more
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Double Dirichlet series and quantum unique ergodicity of weight 1/2 Eisenstein series [PDF]
, 2014 The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for {\Gamma}_0(4) leads to the study of certain double Dirichlet series involving GL2 automorphic forms and Dirichlet characters.
Bailey +9 more
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Dirichlet approximation and universal Dirichlet series
Proceedings of the American Mathematical Society, 2017 We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and {to} the chordal one as well, analogous to classical results of Runge, Mergelyan and Vitushkin. We also strengthen the notion of universal Dirichlet series.
Aron, R.M. +4 more
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Multiple Dirichlet Series for Affine Weyl Groups [PDF]
, 2014 Let $W$ be the Weyl group of a simply-laced affine Kac-Moody Lie group, excepting $\tilde{A}_n$ for $n$ even. We construct a multiple Dirichlet series $Z(x_1, \ldots x_{n+1})$, meromorphic in a half-space, satisfying a group $W$ of functional equations ...
Whitehead, Ian
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Revista de Educación Matemática, 2021 En este artículo estamos interesados en la Teoría Analítica de Números. Ésta tiene diversas maneras tanto de encarar como de resolver problemas. Por ejemplo, a la teoría de números le interesa conocer el comportamiento de ciertas funciones aritméticas (funciones f: N → C), tales como: rk(n) el número de formas de escribir n como suma de k cuadrados; la
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Multiple Lucas–Dirichlet Series Associated With Additive and Dirichlet Characters [PDF]
Mediterranean Journal of Mathematics, 2021 20 ...
N. K. Meher, S. S. Rout
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On Dirichlet series and functional equations
, 2017 There exist many explicit evaluations of Dirichlet series. Most of them are constructed via the same approach: by taking products or powers of Dirichlet series with a known Euler product representation.
Kuznetsov, Alexey
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Illinois Journal of Mathematics, 1960 The work on this paper was done shortly before the author's untimely death in 1957. The editor states that ``while the paper is largely expository and while the principal object of the author was not achieved, the material discussed is significant and seems worth presenting to the mathematical public in order to stimulate further research.'' Suppose ...
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