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Notes on Number Theory

Mathematics
This paper presents a set of survey-style notes linking core themes of pure algebra with central topics in algebraic and analytic number theory. We begin with finite extensions of Q and describe algebraic number fields through their realization as finite-
Miroslav Stoenchev, Slavi Georgiev, Venelin Todorov   +2 more
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On Bohr's theorem for general Dirichlet series

, 2020
Ingo Schoolmann
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Stability and Positivity Preservation in Conventional Methods for Space-Fractional Diffusion Problems: Analysis and Algorithms

Algorithms
The numerical solution of space-fractional diffusion problems is investigated focusing on stability and non-negativity issues. The extension of classical schemes is analyzed for the case of the spectral fractional Dirichlet Laplacian operator.
Menghis T. Bahlibi, Ferenc Izsák
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General Dirichlet series, arithmetic convolution equations and Laplace transforms [PDF]

, 2009
Helge Glöckner, Lutz Lucht, Štefan Porubský   +2 more
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The Geometry of the Mappings by General Dirichlet Series [PDF]

, 2016
Dorin Ghişa
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Variants of a theorem of Helson on general Dirichlet series [PDF]

, 2020
Andreas Defant, Ingo Schoolmann
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General Dirichlet series, arithmetic convolution equations and Laplace transforms [PDF]

, 2007
Helge Glöckner, Lutz Lucht, Štefan Porubský   +2 more
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A Jentzsch-Theorem for Kapteyn, Neumann, and General Dirichlet Series

, 2021
Folkmar Bornemann
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A Jentzsch-Theorem for Kapteyn, Neumann and General Dirichlet Series [PDF]

, 2022
Folkmar Bornemann
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Sets of values of general Dirichlet series

Duke Mathematical Journal, 1968
\textit{Harald Bohr} [Math. Ann. 79, 136--156 (1919; JFM 46.0490.01)] gave four theorems on the set of values of a general Dirichlet series \(f(s) = \sum_{n=1}^\infty a_n e^{-\lambda_ns}\), where \(\lambda_{n+1} > \lambda_n\), \(\lambda_n\to +\infty\), taken along a given vertical line or in its neighborhood.
openaire   +2 more sources