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Experimental Mathematics Volume 12, 2003 - Issue 1
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Original Articles

Complex Dimensions of Self-Similar Fractal Strings and Diophantine Approximation

Michel L. Lapidus Department of Mathematics, University of California, Sproul Hall, Riverside, 92521-0135, California E-mail: [email protected]
&
Machiel van Frankenhuysen Department of Mathematics, Utah Valley State College, Orem, Utah, 84058-5999 E-mail: [email protected]
Pages 41-69 | Published online: 03 Apr 2012

Citations (11)

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E. Dubon & J. M. Sepulcre. (2014) On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials. Experimental Mathematics 23:1, pages 13-24.
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Articles from other publishers (10)

Michel L. Lapidus, Machiel van Frankenhuijsen & Edward K. Voskanian. (2021) Quasiperiodic Patterns of the Complex Dimensions of Nonlattice Self-Similar Strings, via the LLL Algorithm. Mathematics 9:6, pages 591.
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Driss Essouabri & Oswaldo Velásquez Castañón. (2020) Domain of meromorphy of a class of Bateman-like totient zeta functions. Journal of Number Theory 217, pages 102-141.
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Driss Essouabri & Ben Lichtin. (2015) Zeta functions and solutions of Falconer-type problems for self-similar subsets of ℤ n . Proceedings of the London Mathematical Society, pages pdv049.
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G. Mora, J. M. Sepulcre & T. Vidal. (2014) On a conjecture of Lapidus and van Frankenhuysen. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 109:2, pages 747-757.
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G. Mora, J. M. Sepulcre & T. Vidal. (2014) On the existence of fractal strings whose set of dimensions of fractality is not perfect. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 109:1, pages 11-14.
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Michel L. Lapidus, Erin P.J. Pearse & Steffen Winter. (2011) Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators. Advances in Mathematics 227:4, pages 1349-1398.
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Jacques Lévy Véhel & Franklin Mendivil. (2011) Multifractal and higher-dimensional zeta functions. Nonlinearity 24:1, pages 259-276.
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Michel L. Lapidus & Erin P. J. Pearse. (2010) Tube Formulas and Complex Dimensions of Self-Similar Tilings. Acta Applicandae Mathematicae 112:1, pages 91-136.
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Catherine Bénéteau, Brent J. Carswell & Sherwin Kouchekian. (2010) Extremal Problems in the Fock Space. Computational Methods and Function Theory 10:1, pages 189-206.
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Dorin Ervin Dutkay & Palle E.T. Jorgensen. (2007) Fourier frequencies in affine iterated function systems. Journal of Functional Analysis 247:1, pages 110-137.
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