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Transactions of the American Mathematical Society

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Automorphic forms and differentiability properties

Author: Fernando Chamizo
Journal: Trans. Amer. Math. Soc. 356 (2004), 1909-1935
MSC (2000): Primary 42A16, 11F12, 28A80
Published electronically: July 24, 2003
MathSciNet review: 2031046
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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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Additional Information

Fernando Chamizo
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Ciudad Universitaria de Cantoblanco, Madrid 28049, Spain

Received by editor(s): May 14, 2002
Received by editor(s) in revised form: March 27, 2003
Published electronically: July 24, 2003
Article copyright: © Copyright 2003 American Mathematical Society