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October 2020 Iterated towers of number fields by a quadratic map defined over the Gaussian rationals
Yasushi Mizusawa, Kota Yamamoto
Proc. Japan Acad. Ser. A Math. Sci. 96(8): 63-68 (October 2020). DOI: 10.3792/pjaa.96.012

Abstract

An iterated tower of number fields is constructed by adding preimages of a base point by iterations of a rational map. A certain basic quadratic rational map defined over the Gaussian number field yields such a tower of which any two steps are relative bicyclic biquadratic extensions. Regarding such towers as analogues of $\mathbf{Z}_{2}$-extensions, we examine the parity of 2-ideal class numbers along the towers with some examples.

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Yasushi Mizusawa. Kota Yamamoto. "Iterated towers of number fields by a quadratic map defined over the Gaussian rationals." Proc. Japan Acad. Ser. A Math. Sci. 96 (8) 63 - 68, October 2020. https://doi.org/10.3792/pjaa.96.012

Information

Published: October 2020
First available in Project Euclid: 1 October 2020

MathSciNet: MR4155962
Digital Object Identifier: 10.3792/pjaa.96.012

Subjects:
Primary: 11R11
Secondary: 11R23, 11R29

Rights: Copyright © 2020 The Japan Academy

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Vol.96 • No. 8 • October 2020
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