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The Sound of Fractal Strings and the Riemann Hypothesis

In: Analytic Number Theory

Author

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  • Michel L. Lapidus

    (University of California, Department of Mathematics)

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).

Suggested Citation

  • Michel L. Lapidus, 2015. "The Sound of Fractal Strings and the Riemann Hypothesis," Springer Books, in: Carl Pomerance & Michael Th. Rassias (ed.), Analytic Number Theory, pages 201-252, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22240-0_14
    DOI: 10.1007/978-3-319-22240-0_14
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