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Weierstrass fractal drums: II towards a fractal cohomology

Mathematische Zeitschrift, 2024, Vol.308 (2), Article 35

2024

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Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis

Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, 2015-08, Vol.373 (2047), p.20140240

Lapidus, Michel L.

2015

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Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings

2nd ed. 2013, 2012

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Fractal Zeta Functions and Fractal Drums: Higher-Dimensional Theory of Complex Dimensions

1, 2017

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Hyperfunctions and spectral zeta functions of Laplacians on self-similar fractals

Journal of physics. A, Mathematical and theoretical, 2012-09, Vol.45 (36), p.365205-1-365205-14

2012

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Dirac operators and geodesic metric on the harmonic Sierpinski gasket and other fractal sets

Journal of noncommutative geometry, 2014-01, Vol.8 (4), p.947-985

2014

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Minkowski Dimension and Explicit Tube Formulas for p-Adic Fractal Strings

Fractal and fractional, 2018, Vol.2 (4), p.26

2018

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Riemann zeros and phase transitions via the spectral operator on fractal strings

Journal of physics. A, Mathematical and theoretical, 2012-09, Vol.45 (37), p.374005-23

2012

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Adic Fractal Strings of Arbitrary Rational Dimensions and Cantor Strings

P-adic numbers, ultrametric analysis, and applications, 2021, Vol.13 (3), p.215-230

2021

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Horizons of fractal geometry and complex dimensions: 2016 Summer School Fractal Geometry and Complex Dimensions, in celebration of the 60th birthday of Michel Lapidus, June 21-29, 2016, California Polytechnic State University, San Luis Obispo, California

Niemeyer, Robert G

2019

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Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces

Discrete and continuous dynamical systems. Series S, 2019-02, Vol.12 (1), p.105-117

2019

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Progress in Inverse Spectral Geometry

1, 1997

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Nontrivial paths and periodic orbits of the T-fractal billiard table

Nonlinearity, 2016-07, Vol.29 (7), p.2145-2172

2016

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Fractal tube formulas for compact sets and relative fractal drums: oscillations, complex dimensions and fractality

Journal of fractal geometry, 2018-01, Vol.5 (1), p.1-119

2018

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A trace on fractal graphs and the Ihara zeta function

Transactions of the American Mathematical Society, 2009-06, Vol.361 (6), p.3041-3070

2009

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Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings

1. Aufl., 2006

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Quasiperiodic Patterns of the Complex Dimensions of Nonlattice Self-Similar Strings, via the LLL Algorithm

Mathematics (Basel), 2021-03, Vol.9 (6), p.591

2021

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Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions

1, 1999

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Tube Formulas and Complex Dimensions of Self-Similar Tilings

Acta applicandae mathematicae, 2010-10, Vol.112 (1), p.91-136

2010

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Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals

Communications in mathematical physics, 1993-11, Vol.158 (1), p.93-125

1993

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Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis

Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, 2015-08, Vol.373 (2047), p.1-24

Lapidus, Michel L.

2015

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Random fractal strings: Their zeta functions, complex dimensions and spectral asymptotics

Transactions of the American Mathematical Society, 2006-01, Vol.358 (1), p.285-314

2006

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Fractal Strings and Multifractal Zeta Functions

Letters in mathematical physics, 2009-06, Vol.88 (1-3), p.101-129

2009

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Beurling Zeta Functions, Generalised Primes, and Fractal Membranes

Acta applicandae mathematicae, 2006-10, Vol.94 (1), p.21-48

2006

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Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

Advances in mathematics (New York. 1965), 2021-07, Vol.385, p.107771, Article 107771

2021

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Weierstrass fractal drums: II towards a fractal cohomology

Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis

Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings

Fractal Zeta Functions and Fractal Drums: Higher-Dimensional Theory of Complex Dimensions

Hyperfunctions and spectral zeta functions of Laplacians on self-similar fractals

Dirac operators and geodesic metric on the harmonic Sierpinski gasket and other fractal sets

Minkowski Dimension and Explicit Tube Formulas for p-Adic Fractal Strings

Riemann zeros and phase transitions via the spectral operator on fractal strings

Adic Fractal Strings of Arbitrary Rational Dimensions and Cantor Strings

Horizons of fractal geometry and complex dimensions: 2016 Summer School Fractal Geometry and Complex Dimensions, in celebration of the 60th birthday of Michel Lapidus, June 21-29, 2016, California Polytechnic State University, San Luis Obispo, California

Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces

Progress in Inverse Spectral Geometry

Nontrivial paths and periodic orbits of the T-fractal billiard table

Fractal tube formulas for compact sets and relative fractal drums: oscillations, complex dimensions and fractality

A trace on fractal graphs and the Ihara zeta function

Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings

Quasiperiodic Patterns of the Complex Dimensions of Nonlattice Self-Similar Strings, via the LLL Algorithm

Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions

Tube Formulas and Complex Dimensions of Self-Similar Tilings

Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals

Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis

Random fractal strings: Their zeta functions, complex dimensions and spectral asymptotics

Fractal Strings and Multifractal Zeta Functions

Beurling Zeta Functions, Generalised Primes, and Fractal Membranes

Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

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