--- type: Paper Section title: Spectral Geometry — References description: >- Works cited for the Part III chapter: Lapidus's fractal strings and complex dimensions, Flajolet's Mellin transform asymptotics, Faloutsos-Kamel R-tree analysis, Apollonian gaskets and the Riemann Hypothesis, and Zipf's law, with web sources accessed in December 2025. resource: https://tyson-swetnam.github.io/fractal-notebooks/spectral-geometry/references/ tags: [paper, part-iii, reference, spectral-geometry] paper: title: "Spectral Geometry of Fractal Information: Complex Dimensions, the Riemann Zeta Distribution, and Algorithmic Oscillations in Sorting and 2D Packing" part_title: Complex Dimensions and Spectral Geometry landing: https://tyson-swetnam.github.io/fractal-notebooks/spectral-geometry/ stage: chapter-draft sources: - id: drmota-szpankowski2011 resource: https://www.cs.purdue.edu/homes/spa/papers/soda11.pdf title: A master theorem for discrete divide and conquer recurrences (Drmota and Szpankowski 2011, SODA) - id: mackenzie2010 resource: https://www.americanscientist.org/article/a-tisket-a-tasket-an-apollonian-gasket title: A tisket, a tasket, an Apollonian gasket (Mackenzie 2010, American Scientist) - id: hempstead2015 resource: https://scholar.rose-hulman.edu/rhumj/vol16/iss2/13/ title: Apollonian circle packings and the Riemann Hypothesis (Hempstead 2015, Rose-Hulman Undergraduate Mathematics Journal) - id: wiki-apollonian resource: https://en.wikipedia.org/wiki/Apollonian_gasket title: Apollonian gasket (Wikipedia) - id: mathworld-apollonian resource: https://mathworld.wolfram.com/ApollonianGasket.html title: Apollonian gasket (Wolfram MathWorld) - id: faloutsos-kamel1994-pdf resource: https://www-db.disi.unibo.it/courses/SI-M/papers/FK94.pdf title: "Beyond uniformity and independence: analysis of R-trees using the concept of fractal dimension (Faloutsos and Kamel 1994, PDF)" - id: mathoverflow-rh resource: https://mathoverflow.net/questions/17209/consequences-of-the-riemann-hypothesis title: Consequences of the Riemann Hypothesis (MathOverflow) - id: counterfractal resource: https://math.dartmouth.edu/~carlp/counterfractal.pdf title: Counterexamples to the modified Weyl-Berry conjecture on fractal drums (Lapidus and Pomerance, PDF) generated: by: human:tswetnam at: "2025-12-14T00:00:00Z" status: draft --- # References Creative Commons License
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