Results 221 to 230 of about 4,047,455 (275)

On a certain class of dirichlet series

Applicable Analysis, 1990
Summary: For \(0 < a < 1\) and \(\text{Re} (s) > 1\), let \(L(s,a)\) and \(L^* (s,a)\) be the Dirichlet series \(L(s,a) = \sum^\infty_{n = 1} \cos (2 \pi na) n^{-s}\) and \(L^* (s,a) = \sum_{n = 1 }^\infty \sin (2 \pi na) n^{-s}\). We show that \(L(s,a)\) and \(L^*(s,a)\) have holomorphic extension in the whole complex plane. Values of \(L(s,a)\) and \(
exaly   +3 more sources

Composition operators over weighted Bergman spaces of Dirichlet series

Complex Variables and Elliptic Equations, 2022
In the paper ‘Composition operators on weighted Bergman spaces of Dirichlet series. J Math Anal Appl. 2015;426:340–363’, Bailleul completely characterized the boundedness of composition operators on weighted Bergman spaces of Dirichlet series for the ...
Maofa Wang, Min He
semanticscholar   +1 more source

Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values

The Ramanujan journal, 2021
Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its specialization produces new identities and recovers several identities ...
Parth Chavan, Sarth Chavan, C. Vignat, T. Wakhare   +3 more
semanticscholar   +1 more source

Schlicht Dirichlet Series

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. Alexander, has more recently been studied by Remak (5) who has shown that w = ƒ(z), under the hypothesis (1.2), maps |z| < 1 onto a star-like region, and if (1.2) is not satisfied=(z ...
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Moments of real Dirichlet 𝐿-functions and multiple Dirichlet series

We consider the multiple Dirichlet series associated to the 𝑘th moment of real Dirichlet 𝐿-functions, and prove that it has a meromorphic continuation to a specific region in C k + 1 \mathbb{C}^{k+1} , which is conditional under the generalized Lindelöf ...
Martin Čech
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Dirichlet Series

2014
Mathematicians are very interested in prime numbers. In this snapshot, we will discuss some problems concerning the distribution of primes and introduce some special infinite series in order to study them.
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On the Absolute Convergence of Dirichlet Series

The Annals of Mathematics, 1931
This paper contains a complete solution of a problem of great importance for the theory of Dirichlet series, which was formulated by \textit{H. Bohr} [Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1913, 441--488 (1913; JFM 44.0306.01)] but during 18 years resisted the efforts of several mathematicians.
Bohnenblust, H. F., Hille, Einar
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Dirichlet Series and Dirichlet Polynomials

1996
In 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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Hardy Spaces of Dirichlet Series

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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Chebyshev Subspaces of Dirichlet Series

Moscow University Mathematics Bulletin, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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