Proceedings of the American Mathematical Society

Author(s): Keiichi Komatsu
Journal: Proc. Amer. Math. Soc. 128 (2000), 315-323.
MSC (2000): Primary 11G15, 11R27, 11Y40
Posted: September 27, 1999
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Abstract: We consider certain abelian extensions

of $Q(e^{2\pi i/5})$ and show by a method of Shimura that a normal basis of

over

can be given by special values of Siegel modular functions.

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

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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: 10.1090/S0002-9939-99-05601-4
PII: S 0002-9939(99)05601-4
Received by editor(s): June 20, 1997
Posted: September 27, 1999
Communicated by: David E. Rohrlich
Copyright of article: Copyright 1999, American Mathematical Society

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