Integers of the form x2 + ny2

Bumkyu Cho

doi:10.1007/s00605-013-0531-0

Integers of the form x² + ny²

Bumkyu Cho

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We provide a characterization of integers of the form described in the title in the context of class field theory. A more down-to-earth characterization is given when the extended class number is 1, 2, or 3. For completeness we present a formula for the extended class number. Some examples are also given.

Original language	English
Pages (from-to)	195-204
Number of pages	10
Journal	Monatshefte fur Mathematik
Volume	174
Issue number	2
DOIs	https://doi.org/10.1007/s00605-013-0531-0
State	Published - Jun 2014

Keywords

Class field theory
Class numbers
Modular functions
Sums of squares

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10.1007/s00605-013-0531-0

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abstract = "We provide a characterization of integers of the form described in the title in the context of class field theory. A more down-to-earth characterization is given when the extended class number is 1, 2, or 3. For completeness we present a formula for the extended class number. Some examples are also given.",

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AB - We provide a characterization of integers of the form described in the title in the context of class field theory. A more down-to-earth characterization is given when the extended class number is 1, 2, or 3. For completeness we present a formula for the extended class number. Some examples are also given.

KW - Class field theory

KW - Class numbers

KW - Modular functions

KW - Sums of squares

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Integers of the form x² + ny²

Abstract

Keywords

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