On special values of theta functions of genus two

Ehud De Shalit; Eyal Z. Goren

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 3, page 775-799
  • ISSN: 0373-0956

Abstract

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We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.

How to cite

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De Shalit, Ehud, and Goren, Eyal Z.. "On special values of theta functions of genus two." Annales de l'institut Fourier 47.3 (1997): 775-799. <http://eudml.org/doc/75244>.

@article{DeShalit1997,
abstract = {We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.},
author = {De Shalit, Ehud, Goren, Eyal Z.},
journal = {Annales de l'institut Fourier},
keywords = {theta functions; complex multiplication; units},
language = {eng},
number = {3},
pages = {775-799},
publisher = {Association des Annales de l'Institut Fourier},
title = {On special values of theta functions of genus two},
url = {http://eudml.org/doc/75244},
volume = {47},
year = {1997},
}

TY - JOUR
AU - De Shalit, Ehud
AU - Goren, Eyal Z.
TI - On special values of theta functions of genus two
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 3
SP - 775
EP - 799
AB - We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.
LA - eng
KW - theta functions; complex multiplication; units
UR - http://eudml.org/doc/75244
ER -

References

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  3. [G] Eyal Z. GOREN, Ph. D. Thesis, Hebrew University of Jerusalem (1996). 
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  11. [Sh1] G. SHIMURA, Theta Functions with Complex Multiplication, Duke Math. J., 43 (1976), 673-696. Zbl0371.14022MR54 #12664
  12. [Sh2] G. SHIMURA, On Certain Reciprocity Laws for Theta Functions and Modular Forms, Acta Math., 141 (1978), 35-71. Zbl0402.10030MR58 #10757
  13. [Sh3] G. SHIMURA, Arithmetic of Alternating Forms and Quaternion Hermitian Forms, J. Math. Soc. Japan, 15 (1963). Zbl0121.28102MR26 #3694
  14. [Sie] C. L. SIEGEL, Lectures on Advanced Analytic Number Theory, Tata Institute for Fundamental Research (1961). 
  15. [Ta] J. TATE, Les Conjectures de Stark sur les Fonctions L d'Artin en s=0, Progress in Math. vol. 47, Birkhauser (1984). Zbl0545.12009
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  17. [Wa] L. WASHINGTON, Introduction to Cyclotomic Fields, Springer-Verlag, 1982. Zbl0484.12001MR85g:11001

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