A computation of minimal polynomials of special values of Siegel modular functions
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- by Tsuyoshi Itoh PDF
- Math. Comp. 72 (2003), 969-973 Request permission
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
- T. Fukuda and K. Komatsu, On a unit group generated by special values of Siegel modular functions, Math. Comp. 69 (2000), no. 231, 1207–1212. MR 1651753, DOI 10.1090/S0025-5718-99-01118-7
- Keiichi Komatsu, Construction of a normal basis by special values of Siegel modular functions, Proc. Amer. Math. Soc. 128 (2000), no. 2, 315–323. MR 1707153, DOI 10.1090/S0002-9939-99-05601-4
- Goro Shimura, Theta functions with complex multiplication, Duke Math. J. 43 (1976), no. 4, 673–696. MR 424705
Additional Information
- Tsuyoshi Itoh
- Affiliation: Department of Mathematical Sciences, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Email: tsitoh@mn.waseda.ac.jp
- Received by editor(s): March 15, 2000
- Received by editor(s) in revised form: April 10, 2001
- Published electronically: March 22, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 969-973
- MSC (2000): Primary 11G15, 11R27, 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-02-01430-8
- MathSciNet review: 1954979