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Sums of three integral squares in cyclotomic fields

Published online by Cambridge University Press:  17 April 2009

Chun-Gang Ji
Chun-Gang Ji
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, China and Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100080, China, e-mail: cgji@amss.ac.cn
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Abstract

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Let m be an odd positive integer greater than 2 and f the smallest positive integer such that 2f ≡ 1 (mod m). It is proved that every algebraic integer in the cyclotomic field ℚ(ζm) can be expressed as a sum of three integral squares if and only if f is even.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 101 - 106
Copyright
Copyright © Australian Mathematical Society 2003

References

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