The pointwise behavior of Riemann's function

DOI10.4171/jfg/137arXiv2109.08499MaRDI QIDQ6080843

Jasson Vindas, Frederik Broucke

Publication date: 25 October 2023

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.08499

zbMATH Keywords

pointwise Hölder exponentquadratic Gaussian sumsfractional integrals of modular formsRiemann ``non-differentiable function

Mathematics Subject Classification ID

Lipschitz (Hölder) classes (26A16) Continued fractions and generalizations (11J70) Fourier coefficients of automorphic forms (11F30) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Lacunary series of trigonometric and other functions; Riesz products (42A55) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Cites Work

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• Diophantine approximation
• Wo ist die Riemann-Funktion \(\sum_{n=1}^\infty \sin n^ 2 x / n^ 2\) nicht differenzierbar?
• Differentiability of Riemann's function
• Pointwise analysis of Riemann's ``nondifferentiable function
• The spectrum of singularities of Riemann's function
• Riemann's non-differentiable function and the binormal curvature flow
• Geometric differentiability of Riemann's non-differentiable function
• The Hölder exponent of some Fourier series
• Multifractal behavior of polynomial Fourier series
• Some Fourier series with gaps
• Local L^2-regularity of Riemann’s Fourier series
• Intermittency of Riemann’s non-differentiable function through the fourth-order flatness
• On the Hausdorff dimension of Riemann’s non-differentiable function
• On the regularity of fractional integrals of modular forms
• The Differentiability of the Riemann Function at Certain Rational Multiples of &#960
• More on the Differentiability of the Riemann Function
• The Differentiability of Riemann's Function
• Wavelet methods for pointwise regularity and local oscillations of functions

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