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, 2019 This work is dedicated to the study of multiple Dirichlet series and it focuses on three main aspects: convergence, spaces of bounded multiple Dirichlet series and the composition operators of such spaces. In the first chapter we give the necessary preliminary results on regular convergence of double and multiple series and its ...
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Note on Dirichlet and factorial series [PDF]
Transactions of the American Mathematical Society, 1922 openaire +2 more sources
On Kubota's Dirichlet series [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2006 Kubota [19] showed how the theory of Eisenstein series on the higher metaplectic covers of SL2 (which he discovered) can be used to study the analytic properties of Dirichlet series formed with n-th order Gauss sums. In this paper we will prove a functional equation for such Dirichlet series in the precise form required by the companion paper [2 ...
Ben Brubaker, Daniel Bump
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Hardy Spaces of Dirichlet Series [PDF]
, 2013 The forthcoming spaces \( {{\mathcal{H}}^{p}} \) of Dirichlet series (1 ≤ p ≤ ∞), analogous to the familiar Hardy spaces H p on the unit disk, have been successfully introduced to study completeness problems in Hilbert spaces ([63]), first for p = 2, ∞. Later on, the general case was considered in [10] for the study of composition operators.
Hervé Queffélec, Martine Queffélec
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Dirichlet Series and Dirichlet Polynomials
1996In this chapter we define the object of the investigation in our book: the Dirichlet series, the Riemann zeta-function and the Dirichlet L-functions. We also give some classical results concerning the behaviour of these series.
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Probabilistic Methods for Dirichlet Series
2013The title of this chapter is a little emphatic, because the probabilistic methods will here concentrate essentially about one maximal inequality, which is fairly well-known in harmonic analysis, but will have a specific aspect, due to the Bohr point of view on Dirichlet series.
Hervé Queffélec, Martine Queffélec
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Canadian Journal of Mathematics, 1958
For power series (1.1) for which (1.2) , it has been known for four decades (1) that ƒ(z) is regular and univalent or schlicht in |z| < 1. This theorem, due to J. W.
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For power series (1.1) for which (1.2) , it has been known for four decades (1) that ƒ(z) is regular and univalent or schlicht in |z| < 1. This theorem, due to J. W.
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Journal of Soviet Mathematics, 1979
Two theorems are proved on Dirichlet series of a special type related to multiplicative functions f(n), ¦f(n)¦⩽1. These theorems develop well-known results of Halasz (G. Halasz, Acta Math. Acad. Sci. Hungar.,19, Nos. 3–4, 365#x2013;404 (1968)).
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Two theorems are proved on Dirichlet series of a special type related to multiplicative functions f(n), ¦f(n)¦⩽1. These theorems develop well-known results of Halasz (G. Halasz, Acta Math. Acad. Sci. Hungar.,19, Nos. 3–4, 365#x2013;404 (1968)).
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Universality and summability of Dirichlet series
Complex Variables and Elliptic Equations, 2009We show genericity and algebraic genericity of Dirichlet series, whose given matrix transform has universal properties. Conversely, for any given formal Dirichlet series L with non-zero coefficients, we construct a matrix A, so that the A-transform of L is universal. This extends results of Bernal-Gonzalez, Calderon-Moreno and Luh.
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