Automorphic forms and differentiability properties

Chamizo, Fernando

doi:10.1090/S0002-9947-03-03349-X

Automorphic forms and differentiability properties
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by Fernando Chamizo

Trans. Amer. Math. Soc. 356 (2004), 1909-1935

DOI: https://doi.org/10.1090/S0002-9947-03-03349-X

Published electronically: July 24, 2003

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Abstract:

We consider Fourier series given by a type of fractional integral of automorphic forms, and we study their local and global properties, especially differentiability and fractal dimension of the graph of their real and imaginary parts. In this way we can construct fractal objects and continuous non-differentiable functions associated with elliptic curves and theta functions.

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