Arithmetic Hilbert modular functions (II).

Baily 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 -