Riemann Hypothesis and Inverse Spectral Problems

  • Michel L. Lapidus
  • Machiel van Frankenhuijsen
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter, we provide an alternative formulation of the Riemann hypothesis in terms of a natural inverse spectral problem for fractal strings. After stating this inverse problem in Section 9.1, we show in Section 9.2 that its solution is equivalent to the nonexistence of critical zeros of the Riemann zeta function on a given vertical line.


Zeta Function Complex Dimension Riemann Zeta Function Riemann Hypothesis Inverse Spectral Problem 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Michel L. Lapidus
    • 1
  • Machiel van Frankenhuijsen
    • 2
  1. 1.Department of MathematicsUniversity of California, RiversideRiversideUSA
  2. 2.Department of MathematicsUtah Valley UniversityOremUSA

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