Arithmetic Hilbert Modular Functions, II.

Autores: Walter L. Baily
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 1, Nº 1, 1985, págs. 85-119
Idioma: inglés
DOI: 10.4171/rmi/4
Títulos paralelos:
- Funciones modulares de Hilbert aritméticas (II).
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Resumen
- The purpose of this paper, which is a continuation of [2, 3], is to prove further results about arithmetic modular forms and functions. In particular we shall demonstrate here a q-expansion principle which will be useful in proving a reciprocity law for special values of arithmetic Hilbert modular functions, of which the classical results on complex multiplication are a special case. The main feature of our treatment is, perhaps, its independence of the theory of abelian varieties.