Abstract
Our aim in this note is to point out that the complex numbers which parameterize the even Maass forms on the modular group S L(2, Z) are generalized Hausdorff, or fractal, dimensions of the set of irrationals, when the latter is appropriately viewed as a multifractal.
Based on lectures given at Oberwolfach (1993) and MSRI (1994).
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References
I. Efrat, Dynamics of the continued fraction map and the spectral theory of S L (2, Z), Invent. Math., vol. 114 (1993), 207–218.
M. Feigenbaum, Presentation functions, fixed points and the theory of scaling function dynamics, J. of Stat. Phys., vol. 52 (1988), 527–569.
J. Lewis, Spaces of holomorphic functions equivalent to the even Maass cusp forms, Invent. Math., vol. 127, no. 2 (1997).
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Efrat, I. (1999). Multifractal Spectrum and Laplace Spectrum. In: Hejhal, D.A., Friedman, J., Gutzwiller, M.C., Odlyzko, A.M. (eds) Emerging Applications of Number Theory. The IMA Volumes in Mathematics and its Applications, vol 109. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1544-8_7
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DOI: https://doi.org/10.1007/978-1-4612-1544-8_7
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