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We discuss the asymptotic behavior of Fourier transforms of Cantor measures and wavelets, and related functions that might be called multiperiodic because they satisfy a simple recursion relation involving a blend of additive and multiplicative structures.
Our numerical experiments motivated conjectures about this asymptotic behavior, some of which we can prove. We describe the experiments, the proofs, and several remaining conjectures and open problems. We also contribute to the evolving iconography of fractal mathematics by presenting the numerical evidence in graphical form.
This article provides a glimpse into "arithmetical quantum chaos'' through a study of the topography and statistical properties of the eigenfunctions of the Laplacian for the modular surface $\PSL(2,\ints)\bs H$.
We outline an approach for the computation of a good candidate for the generating function of a power series for which only the first few coefficients are known. More precisely, if the derivative, the logarithmic derivative, the reversion, or another transformation of a given power series (even with polynomial coefficients) appears to admit a rational generating function, we compute the generating function of the original series by applying the inverse of those transformations to the rational generating function found.