# Arithmetic Hilbert modular functions (II).

Revista Matemática Iberoamericana (1985)

- Volume: 1, Issue: 1, page 85-119
- ISSN: 0213-2230

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topBaily Jr., Walter L.. "Arithmetic Hilbert modular functions (II).." Revista Matemática Iberoamericana 1.1 (1985): 85-119. <http://eudml.org/doc/39312>.

@article{BailyJr1985,

abstract = {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.},

author = {Baily Jr., Walter L.},

journal = {Revista Matemática Iberoamericana},

keywords = {Teoría algebraica de números; Funciones modulares de Hilbert; Formas modulares; Multiplicación compleja; Hilbert modular functions; arithmetic Hilbert modular forms; q-expansion principle; reciprocity laws; special values; graded algebra; Shimura's reciprocity law},

language = {eng},

number = {1},

pages = {85-119},

title = {Arithmetic Hilbert modular functions (II).},

url = {http://eudml.org/doc/39312},

volume = {1},

year = {1985},

}

TY - JOUR

AU - Baily Jr., Walter L.

TI - Arithmetic Hilbert modular functions (II).

JO - Revista Matemática Iberoamericana

PY - 1985

VL - 1

IS - 1

SP - 85

EP - 119

AB - 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.

LA - eng

KW - Teoría algebraica de números; Funciones modulares de Hilbert; Formas modulares; Multiplicación compleja; Hilbert modular functions; arithmetic Hilbert modular forms; q-expansion principle; reciprocity laws; special values; graded algebra; Shimura's reciprocity law

UR - http://eudml.org/doc/39312

ER -

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