Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
DE
EN
Books
Journals
Events
Topic Page
Marketing
Log in
Learn more about individual access
Request company access
13th International Engine Congress 2026 | 24 + 25 February 2026

Meeting Place for the Powertrain and Sustainable Fuels Community

Take part as a speaker in the 13th International Engine Congress 2026, the Meeting Place for the Powertrain, and Sustainable Fuels Community for the exchange of experience. Submit a subject proposal online about our main subject areas: Passenger car engine technology, Commercial vehicle engine technology and Sustainable Fuels & Energy!
EXTENDED SEARCH
Log in
Top
Published in:
Read chapter Read first chapter

2024 | OriginalPaper | Chapter

A Note on Sums of Squares in Non-Totally Real Fields

Author : Srijonee Shabnam Chaudhury

Published in: Class Groups of Number Fields and Related Topics

Publisher: Springer Nature Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Let K be any non-totally real number field and \(\mathcal {O}_K\) be its ring of integers. Let \(m_K\) be the smallest positive integer such that every element of \(m_K \mathcal {O}_K \) can be written as sums of integral squares. We have shown that \(m_K \le 4\).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter A Brief Survey of Recent Results on Pólya Groups
next chapter Can a k-Lucas Number be a Product of Two Fermat Numbers?
Literature
1.
Lagrange, J.L.: Démonstration d’un théoréme d’arithmétique. Nouveaux Mém. Acad. Roy. Sci. Belles-Lettres Berlin 1770, reprinted in: Œuvres 3 (1869), 189–201
2.
3.
Siegel, C.L.: Sums of $m$-th powers of algebraic integers. Ann. Math. 46, 313–339 (1945)
4.
Moser, C.: Représentation de negative 1$-1$ par une somme de carrés dans certain corps locaux et globaux, et dans certains anneaux d’entiers algebriques. C. R. Acad. Sci. Paris Ser. A-B 271, A1200–A1203 (1970)
5.
Estes, D.R., Hsia, J.S.: Sums of three integral squares in complex quadratic fields. Proc. Am. Math. Soc. 89, 211–214 (1983)CrossRef
6.
Ji, C.-G., Wang, Y.H., Xu, F.: Sums of three squares over imaginary quadratic fields. Forum Math. 18, 585–601 (2006)MathSciNetCrossRef
7.
8.
9.
Moser, C.: Représentation de -1 comme somme de cart-k dans un corps cyclotomique quelconque. J. Number Theory 5, 139–141 (1973)MathSciNetCrossRef
10.
Ji, C.-G., Wei, D.S.: Sums of integral squares in cyclotomic fields. C. R. Acad. Sci. Paris Ser. I(344), 413–416 (2007)MathSciNetCrossRef
11.
Lam, T.Y.: The Algebraic Theory of Quadratic Forms. Benjamin, Reading, Mass (1973)
12.
13.
Peters, M.: Summe von Quadraten in Zahlringen. J. Reine Angew. Math. 268(269), 318–323 (1974)MathSciNet
14.
Lewis, D.W.: On the level. IMS Bull. 19, 33–48 (1987)
15.
Denert, M., Tignol, J.P., Van Geel, J., Vast, N.: The level of cyclic division algebras. Math. Z. 205, 603–616 (1990)MathSciNetCrossRef
16.
17.
Brocker, L., Dress, A., Scharlau: An (almost trivial) local global principle for the representation of -1 as a sum of squares in an arbitrary commutative ring (1982)
Metadata
Title
A Note on Sums of Squares in Non-Totally Real Fields
Author
Srijonee Shabnam Chaudhury
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Class Groups of Number Fields and Related Topics

Print ISBN: 978-981-9769-10-0

Electronic ISBN: 978-981-9769-11-7

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-6911-7_13

Premium Partner

    Image Credits