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Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function

About this Title

Christina Q. He and Michel L. Lapidus

Publication: Memoirs of the American Mathematical Society
Publication Year 1997: Volume 127, Number 608
ISBNs: 978-0-8218-0597-8 (print); 978-1-4704-0193-1 (online)
MathSciNet review: 1376743
MSC: Primary 35P20; Secondary 11M06, 28A80, 58G25

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Table of Contents


  • 1. Introduction
  • 2. Statement of the main results
  • 3. Sharp error estimates and their converse when $n$ = 1
  • 4. Spectra of fractal strings and the Riemann zeta-function
  • 5. The complex zeros of the Riemann zeta-function
  • 6. Error estimates for $n \geq 2$
  • 7. Examples
  • Appendix. Examples of gauge functions
American Mathematical Society