On a unit group generated by special values of Siegel modular functions
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- by T. Fukuda and K. Komatsu PDF
- Math. Comp. 69 (2000), 1207-1212 Request permission
Abstract:
There has been important progress in constructing units and $S$-units associated to curves of genus 2 or 3. These approaches are based mainly on the consideration of properties of Jacobian varieties associated to hyperelliptic curves of genus 2 or 3. In this paper, we construct a unit group of the ray class field $k_6$ of $\mathbb {Q}(\exp (2\pi i/5))$ modulo 6 with full rank by special values of Siegel modular functions and circular units. We note that $k_6=\mathbb {Q}(\exp (2\pi i/15), \sqrt [5]{-24} )$. Our construction of units is number theoretic, and closely based on Shimura’s work describing explicitly the Galois actions on the special values of theta functions.References
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Additional Information
- T. Fukuda
- Affiliation: Department of Mathematics, College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, Japan
- Email: fukuda@math.cit.nihon-u.ac.jp
- K. Komatsu
- Affiliation: Department of Information and Computer Science, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169, Japan
- Email: kkomatsu@mn.waseda.mse.jp
- Received by editor(s): October 16, 1997
- Received by editor(s) in revised form: August 14, 1998
- Published electronically: February 19, 1999
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 1207-1212
- MSC (1991): Primary 11G15, 11R27, 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-99-01118-7
- MathSciNet review: 1651753