## Automorphic forms and differentiability properties

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- by Fernando Chamizo PDF
- Trans. Amer. Math. Soc.
**356**(2004), 1909-1935 Request permission

## 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.## References

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## Additional Information

**Fernando Chamizo**- Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Ciudad Universitaria de Cantoblanco, Madrid 28049, Spain
- Email: fernando.chamizo@uam.es
- Received by editor(s): May 14, 2002
- Received by editor(s) in revised form: March 27, 2003
- Published electronically: July 24, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**356**(2004), 1909-1935 - MSC (2000): Primary 42A16, 11F12, 28A80
- DOI: https://doi.org/10.1090/S0002-9947-03-03349-X
- MathSciNet review: 2031046