Mathematics of Computation

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A computation of minimal polynomials of special values of Siegel modular functions

Author(s): Tsuyoshi Itoh.
Journal: Math. Comp. 72 (2003), 969-973.
MSC (2000): Primary 11G15, 11R27, 11Y40
Posted: March 22, 2002
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Abstract | References | Similar articles | Additional information

Abstract: Recently, Fukuda and Komatsu constructed units of a certain abelian extension of $\mathbb{Q}(\exp(2 \pi \sqrt{-1}/5))$ using special values of Siegel modular functions. In this paper, we determine the minimal polynomials of these units.

References:

[FK]: T. Fukuda and K. Komatsu: On a unit group generated by special values of Siegel modular functions, Math. Comp. 69 (2000), 1207-1212. MR 2000j:11089
[K]: K. Komatsu: Construction of normal basis by special values of Siegel modular functions, Proc. Amer. Math. Soc., 128 (2000), 315-323. MR 2000d:11139
[S]: G. Shimura: Theta functions with complex multiplication,Duke Math. J. 43 (1976), 673-696. MR 54:12664


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