Special values of Hilbert modular functions.

Martin L. Karel

Revista Matemática Iberoamericana (1986)

  • Volume: 2, Issue: 4, page 367-380
  • ISSN: 0213-2230

Abstract

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Recently, Baily has established new foundation for complex multiplication in the context of Hilbert modular functions; see [1]-[4]. However, in his treatment there is a restriction on the class of CM-points treated. Namely, the order of complex multiplications associated to the point must be the maximal order in its quotient field. The purpose of this paper is two-fold: (1) to remove the restriction just mentioned; (2) to recover a result of Tate on the conjugates of CM-points by arbitrary Galois automorphisms of Q' (the algebraic closure of Q). This is done without the use of moduli.

How to cite

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Karel, Martin L.. "Special values of Hilbert modular functions.." Revista Matemática Iberoamericana 2.4 (1986): 367-380. <http://eudml.org/doc/39334>.

@article{Karel1986,
abstract = {Recently, Baily has established new foundation for complex multiplication in the context of Hilbert modular functions; see [1]-[4]. However, in his treatment there is a restriction on the class of CM-points treated. Namely, the order of complex multiplications associated to the point must be the maximal order in its quotient field. The purpose of this paper is two-fold: (1) to remove the restriction just mentioned; (2) to recover a result of Tate on the conjugates of CM-points by arbitrary Galois automorphisms of Q' (the algebraic closure of Q). This is done without the use of moduli.},
author = {Karel, Martin L.},
journal = {Revista Matemática Iberoamericana},
keywords = {Funciones modulares; Cuerpos; special values of arithmetic Hilbert modular functions; complex multiplications; Galois automorphisms; CM-points},
language = {eng},
number = {4},
pages = {367-380},
title = {Special values of Hilbert modular functions.},
url = {http://eudml.org/doc/39334},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Karel, Martin L.
TI - Special values of Hilbert modular functions.
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 4
SP - 367
EP - 380
AB - Recently, Baily has established new foundation for complex multiplication in the context of Hilbert modular functions; see [1]-[4]. However, in his treatment there is a restriction on the class of CM-points treated. Namely, the order of complex multiplications associated to the point must be the maximal order in its quotient field. The purpose of this paper is two-fold: (1) to remove the restriction just mentioned; (2) to recover a result of Tate on the conjugates of CM-points by arbitrary Galois automorphisms of Q' (the algebraic closure of Q). This is done without the use of moduli.
LA - eng
KW - Funciones modulares; Cuerpos; special values of arithmetic Hilbert modular functions; complex multiplications; Galois automorphisms; CM-points
UR - http://eudml.org/doc/39334
ER -

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