Picard-Shimura class fields corresponding to a family of hyperelliptic curves

DOI10.1007/s12188-015-0109-yzbMath1398.11093OpenAlexW588767607MaRDI QIDQ892150

Thorsten Riedel

Publication date: 18 November 2015

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12188-015-0109-y

zbMATH Keywords

hyperelliptic curvesmodular formscomplex multiplicationclass fields

Mathematics Subject Classification ID

Complex multiplication and moduli of abelian varieties (11G15) Class field theory (11R37) Complex multiplication and abelian varieties (14K22)

Cites Work

• An extended Gauss AGM and corresponding Picard modular forms
• On the representation of the Picard modular function by \(\theta\) constants. I-II
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• On the Construction of Class Fields by Picard Modular Forms
• On Abelian Varieties with Complex Multiplication
• Determination of all imaginary abelian sextic number fields with class number ≤ 11
• The imaginary cyclic sextic fields with class numbers equal to their genus class numbers
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