The Sound of Fractal Strings and the Riemann Hypothesis

Michel L. Lapidus ()
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Michel L. Lapidus: University of California, Department of Mathematics

A chapter in Analytic Number Theory, 2015, pp 201-252 from Springer

Abstract: Abstract We give an overview of the intimate connections between natural direct and inverse spectral problems for fractal strings, on the one hand, and the Riemann zeta function and the Riemann hypothesis, on the other hand (in joint works of the author with Carl Pomerance and Helmut Maier, respectively). We also briefly discuss closely related developments, including the theory of (fractal) complex dimensions (by the author and many of his collaborators, including especially Machiel van Frankenhuijsen), quantized number theory and the spectral operator (jointly with Hafedh Herichi), and some other works of the author (and several of his collaborators).

Keywords: Riemann zeta function; Riemann hypothesis (RH); Quantization; Quantized number theory; Fractal strings; Geometry and spectra; Direct and inverse spectral problems for fractal strings; Minkowski dimension; Minkowski measurability; Complex dimensions; Weyl–Berry conjecture; Fractal drums; Infinitesimal shift; Spectral operator; Invertibility; Quantized Dirichlet series and Euler product; Universality; Phase transitions; Symmetric and asymmetric criteria for RH (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22240-0_14

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DOI: 10.1007/978-3-319-22240-0_14

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