Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Construction of a normal basis by special values of Siegel modular functions


Author: Keiichi Komatsu
Journal: Proc. Amer. Math. Soc. 128 (2000), 315-323
MSC (2000): Primary 11G15, 11R27, 11Y40
DOI: https://doi.org/10.1090/S0002-9939-99-05601-4
Published electronically: September 27, 1999
MathSciNet review: 1707153
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider certain abelian extensions $K,k_1$ of $Q(e^{2\pi i/5})$ and show by a method of Shimura that a normal basis of $K$ over $k_1$ can be given by special values of Siegel modular functions.


References [Enhancements On Off] (What's this?)

  • 1. J. Igusa, Arithmetic variety of moduli for genus two, Ann. Math. 72 (1960), 612-649. MR 22:5637
  • 2. J. Igusa, Modular forms and projective invariants, Amer. J. Math. 89 (1967), 817-855. MR 37:5217
  • 3. J. Igusa, On the ring of modular forms of degree two over $\mathbb{Z}$, Amer. J. Math. 101 (1979), 149-183. MR 80d:10039
  • 4. F. Kawamoto, On normal integral bases, Tokyo J. Math. 7 (1984), 221-231. MR 87b:11112
  • 5. K. Komatsu, Normal basis and Greenberg's conjecture, Math. Ann. 300 (1994), 157-163. MR 95i:11129
  • 6. T. Okada, Normal bases of class field over Gauss number field, J. London Math. Soc. 22 (1980), 221-225. MR 83b:10041
  • 7. R. Schertz, Galoismodulstruktur und Elliptische Funktionen, J. Number Theory 39 (1991), 285-326. MR 92j:11130
  • 8. G. Shimura, Theta functions with complex multiplication, Duke Math. J. 43 (1976), 673-696. MR 54:12664
  • 9. G. Shimura, On canonical models of arithmetic quotients of bounded symmetric domains I, II, Ann. of Math. 91 (1970), 144-222; 92 (1970), 528-549. MR 41:1686; MR 45:1840
  • 10. G. Shimura, Y. Taniyama, Complex multiplication of abelian varieties and its application to number theory, Publ. Math. Soc. Japan 6 (1961). MR 23:A2419
  • 11. M. J. Taylor, Relative Galois module structure of rings of integers and elliptic functions II, Ann. Math. 121 (1985), 519-535. MR 87e:11130a

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11G15, 11R27, 11Y40

Retrieve articles in all journals with MSC (2000): 11G15, 11R27, 11Y40


Additional Information

Keiichi Komatsu
Affiliation: Department of Information and Computer Science, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169, Japan

DOI: https://doi.org/10.1090/S0002-9939-99-05601-4
Received by editor(s): June 20, 1997
Published electronically: September 27, 1999
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society