The convergence of certain Diophantine series

DOI10.1016/j.jnt.2021.04.022zbMath1479.11125OpenAlexW3169897912WikidataQ114156977 ScholiaQ114156977MaRDI QIDQ1981592

Bruno Martin, Fernando Chamizo

Publication date: 6 September 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2021.04.022

zbMATH Keywords

Lipschitz regularityapproximate functional equationDiophantine series

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Singular functions, Cantor functions, functions with other special properties (26A30) Other Dirichlet series and zeta functions (11M41) Continued fractions and generalizations (11J70)

Related Items (1)

The approximate functional equation of some Diophantine series

Cites Work

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• The spectrum of singularities of Riemann's function
• On certain approximate functional equations that are related to the Gauss transformation
• Multifractal behavior of polynomial Fourier series
• Special values of trigonometric Dirichlet series and Eichler integrals
• On the convergence of Diophantine Dirichlet series
• Comportement local moyen de la fonction de Brjuno
• On the regularity of fractional integrals of modular forms
• Estimates of $\sum__{k=1}^N k^{-s}〈kx〉^{-t}$

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