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June 2011 Sum of three squares and class numbers of imaginary quadratic fields
Peter Jaehyun Cho
Proc. Japan Acad. Ser. A Math. Sci. 87(6): 91-94 (June 2011). DOI: 10.3792/pjaa.87.91

Abstract

For a positive integer $k$ and a certain arithmetic progression $A$, there exist infinitely many quadratic fields $\mathbf{Q}(\sqrt{-d})$ whose class numbers are divisible by $k$ and $d\in A$. From this, we have a linear congruence of the representation numbers of integers as sums of three squares.

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Peter Jaehyun Cho. "Sum of three squares and class numbers of imaginary quadratic fields." Proc. Japan Acad. Ser. A Math. Sci. 87 (6) 91 - 94, June 2011. https://doi.org/10.3792/pjaa.87.91

Information

Published: June 2011
First available in Project Euclid: 1 June 2011

zbMATH: 1256.11058
MathSciNet: MR2803887
Digital Object Identifier: 10.3792/pjaa.87.91

Subjects:
Primary: 11R11 , 11R29

Keywords: arithmetic progression , Class number , imaginary quadratic field , Sum of three squares

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 6 • June 2011
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