The Sound of Fractal Strings and the Riemann Hypothesis

DOI10.1007/978-3-319-22240-0_14zbMath1336.28004arXiv1505.01548OpenAlexW1513290168MaRDI QIDQ2800637

Michel L. Lapidus

Publication date: 18 April 2016

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

Full work available at URL: https://arxiv.org/abs/1505.01548

zbMATH Keywords

Riemann zeta functionquantizationinvertibilityspectral operatorMinkowski measurabilitycomplex dimensionsfractal stringsWeyl-Berry conjecturefractal drumsdirect and inverse spectral problems for fractal stringsgeometry and spectrainfinitesimal shiftquantized Dirichlet series and Euler productquantized number theoryRiemann hypothesis (RH)symmetric and asymmetric criteria for RH

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80)

Related Items (4)

Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a spectral analysis for the Sierpiński gasket.
• Can one hear the dimension of a fractal?
• The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
• Werteverteilung von Zetafunktionen
• Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary
• A joint universality theorem for Dirichlet L-functions
• A sharp asymptotic remainder estimate for the eigenvalues of the Laplacian in a domain of \(R^3\)
• Brownian motion on a random recursive Sierpinski gasket
• On the asymptotics of the eigenvalue counting function for random recursive Sierpinski gaskets
• Perturbation theory for linear operators.
• Eigenfunctions of the Koch snowflake domain
• On spectral asymptotics for domains with fractal boundaries
• The spectral function of an elliptic operator
• Removable singularities of solutions of linear partial differential equations
• On the existence of exponential polynomials with prefixed gaps
• Multifractal and higher-dimensional zeta functions
• On volume and surface area of parallel sets
• The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums
• An Estimate Near the Boundary for the Spectral Function of the Laplace Operator
• Meillieurs estimations asymptotiques des restes de la fonctionn spectrale et des valeurs propres relatifs au laplacien.
• Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture
• A Comparison Estimate for the Heat Equation with an Application to the Heat Content of the S -Adic Von Koch Snowflake
• SNOWFLAKE HARMONICS AND COMPUTER GRAPHICS: NUMERICAL COMPUTATION OF SPECTRA ON FRACTAL DRUMS
• Lefschetz trace formulas and explicit formulas in analytic number theory.
• An Example of a Two-Term Asymptotics for the "Counting Function" of a Fractal Drum
• On the Minkowski Measurability of Fractals
• The Riemann Hypothesis and Inverse Spectral Problems for Fractal Strings
• Counterexamples to the modified Weyl–Berry conjecture on fractal drums
• Spectral analysis of a self-similar Sturm-Liouville operator
• The zeta function of the Laplacian on certain fractals
• Random fractal strings: Their zeta functions, complex dimensions and spectral asymptotics
• On the Non-Periodicity of the Zeros of the Riemann Zeta-Function
• On the Complementary Intervals of a Linear Closed Set of Zero Lebesgue Measure
• Remarks on Periodic Sequences and the Riemann Zeta-Function
• Integrated density of states of self-similar Sturm-Liouville operators and holomorphic dynamics in higher dimension.

This page was built for publication: The Sound of Fractal Strings and the Riemann Hypothesis