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Automorphic forms

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Abstract

Definition 2.3.4 allows too huge a space of automorphic forms to be convenient. In this chapter we formulate our concept of ‘automorphic form with growth condition’. In 1.7.1 we have already indicated that we want to allow singularities above a finite set in \(Y = \tilde \Gamma \backslash h\). In 3.5.1 we have fixed this set as P Y , the set of ‘interior exceptional points’. Moreover, we want to impose growth conditions at all points of P = P Y ∪ {cusps}.

Keywords

  • Modular Form
  • Fourier Expansion
  • Cusp Form
  • Automorphic Form
  • Polynomial Growth

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© 1994 Springer Basel AG

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Bruggeman, R.W. (1994). Automorphic forms. In: Families of Automorphic Forms. Modern Birkhäuser Classics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0346-0336-2_4

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  • DOI: https://doi.org/10.1007/978-3-0346-0336-2_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0346-0335-5

  • Online ISBN: 978-3-0346-0336-2

  • eBook Packages: Springer Book Archive