Downloads
Papers
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The ABC Conjecture Implies Roth's Theorem and Mordell's Conjecture [PDF]
Matematica Contemporanea 16 (1999), 45-72.
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Arithmetic Progressions of Zeros of the Riemann Zeta Function [PDF]
J. of Number Theory 115 (2005), 360-370.
Programs
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First set of maple programs that produce diagrams of the complex dimensions of fractal strings.
`Init' files are for the different strings, for example init.234 contains data for the string
with scaling ratios 1/2, 1/3, 1/4.
The .m files are maple files, containing the result of computations, like the roots of a
polynomial of degree 4000.
These programs were used to produce the diagrams for the Exp. Math. paper Complex Dimensions of Self-Similar Fractal Strings and Diophantine Approximation [PDF].
Programs [TAR]
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Second set of maple programs that produce diagrams of the complex dimensions of fractal strings
and density-of-real-parts graphs. The files sqrt2 etc. contain data for the strings, sqrt2
is nongeneric nonlattice, the other two generic. The prefixes c, d, l, s stand for
complex dimensions, density graph, large diagram of cxd, small diagram of cxd, the last two in
combination with a density diagram.
These programs are slightly better documented and slightly easier to understand. And they
allow much more flexibility of the paper size, size of diagram etc.
These programs were used to produce the diagrams for Fractality, Self-Similarity and Complex Dimensions [PDF],
in the book Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot.
New programs [TAR]
Copyright 2005 Machiel van Frankenhuijsen.
All rights reserved.
All rights reserved.