The next Pellian equation

The pellian equations x2−dy2=−4 in Z or ξ2∂n2=4i in Z[i] both have similar criteria of solvability according to factors of 2 or 4 in the class number for $$\mathbb{Q}(\surd - p)$$ , when a prime p=d or Na. The next pellian equation leads to a tower of pellian equations whose height limits the power...

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Bibliographic Details
Published inAnalytic Number Theory pp. 221 - 230
Main Author Cohn, Harvey
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 21.10.2006
SeriesLecture Notes in Mathematics
Subjects
Algebraic Number Field
Class Field
Class Field Theory
Class Number
Congruence Condition
Online AccessGet full text
ISBN9783540111733
3540111735
ISSN0075-8434
1617-9692
DOI10.1007/BFb0096463

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Summary:The pellian equations x2−dy2=−4 in Z or ξ2∂n2=4i in Z[i] both have similar criteria of solvability according to factors of 2 or 4 in the class number for $$\mathbb{Q}(\surd - p)$$ , when a prime p=d or Na. The next pellian equation leads to a tower of pellian equations whose height limits the power of 2 dividing that class number.
Bibliography:Research supported by NSF Grant MCS 7903060.
Original Abstract: The pellian equations x2−dy2=−4 in Z or ξ2∂n2=4i in Z[i] both have similar criteria of solvability according to factors of 2 or 4 in the class number for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{Q}(\surd - p)$$\end{document}, when a prime p=d or Na. The next pellian equation leads to a tower of pellian equations whose height limits the power of 2 dividing that class number.
Affectionately dedicated to Emil Grosswald in appreciation of his enthusiasm for concrete results
ISBN:9783540111733
3540111735
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0096463