Skip to main content
Top

2013 | OriginalPaper | Chapter

Integral Positive Ternary Quadratic Forms

Author : William C. Jagy

Published in: Quadratic and Higher Degree Forms

Publisher: Springer New York

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

search-config
loading …

Abstract

We discuss some families of integral positive ternary quadratic forms. Our main example is \(f(x,y,z) = {x}^{2} + {y}^{2} + 16n{z}^{2},\) where n is positive, squarefree, and \(n = {u}^{2} + {v}^{2}\) with \(u,v \in \mathbf{Z}.\)

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!

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!

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!

Literature
1.
go back to reference J.W. Benham, A. G. Earnest, J. S. Hsia, and D. C. Hung. Spinor regular positive ternary quadratic forms. Journal of the London Mathematical Society, 42:1–10, 1990.MathSciNetMATHCrossRef J.W. Benham, A. G. Earnest, J. S. Hsia, and D. C. Hung. Spinor regular positive ternary quadratic forms. Journal of the London Mathematical Society, 42:1–10, 1990.MathSciNetMATHCrossRef
2.
go back to reference J.W. Benham and J. S. Hsia. On spinor exceptional representations. Nagoya Mathematical Journal, 87:247–260, 1982.MathSciNetMATH J.W. Benham and J. S. Hsia. On spinor exceptional representations. Nagoya Mathematical Journal, 87:247–260, 1982.MathSciNetMATH
3.
go back to reference A. Berkovich. Personal communication, 2010. A. Berkovich. Personal communication, 2010.
4.
go back to reference H. Brandt and O. Intrau. Tabelle reduzierten positiver ternärer quadratischer Formen. Abh. der Sächsischen Akad. der Wissenschaften zu Leipzig, Math.-Naturw., 45(4), 1958. H. Brandt and O. Intrau. Tabelle reduzierten positiver ternärer quadratischer Formen. Abh. der Sächsischen Akad. der Wissenschaften zu Leipzig, Math.-Naturw., 45(4), 1958.
5.
go back to reference W. K. Chan. Personal communication, 2008. One page pdf. W. K. Chan. Personal communication, 2008. One page pdf.
6.
go back to reference W. Duke and R. Schulze-Pillot. Representations of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids. Inventiones Mathematicae, 99:49–57, 1990.MathSciNetMATHCrossRef W. Duke and R. Schulze-Pillot. Representations of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids. Inventiones Mathematicae, 99:49–57, 1990.MathSciNetMATHCrossRef
7.
go back to reference A. G. Earnest, J. S. Hsia, and D. C. Hung. Primitive representations by spinor genera of ternary quadratic forms. Journal of the London Mathematical Society, 50:222–230, 1994.MathSciNetMATHCrossRef A. G. Earnest, J. S. Hsia, and D. C. Hung. Primitive representations by spinor genera of ternary quadratic forms. Journal of the London Mathematical Society, 50:222–230, 1994.MathSciNetMATHCrossRef
9.
go back to reference J. S. Hsia. Personal communication, 2004. J. S. Hsia. Personal communication, 2004.
10.
11.
go back to reference B. W. Jones and G. Pall. Regular and semi-regular positive ternary quadratic forms. Acta Mathematica, 70:165–191, 1939.MathSciNetCrossRef B. W. Jones and G. Pall. Regular and semi-regular positive ternary quadratic forms. Acta Mathematica, 70:165–191, 1939.MathSciNetCrossRef
12.
go back to reference I. Kaplansky. Notes on the classification of regular ternary forms. Unpublished, 1996. I. Kaplansky. Notes on the classification of regular ternary forms. Unpublished, 1996.
14.
go back to reference R. Schulze-Pillot. Darstellungsmaße von Spinorgeschlechtern ternärer quadratischer Formen. J. Riene Angew. Math., 352:114–132, 1984.MathSciNetMATH R. Schulze-Pillot. Darstellungsmaße von Spinorgeschlechtern ternärer quadratischer Formen. J. Riene Angew. Math., 352:114–132, 1984.MathSciNetMATH
15.
go back to reference G. L. Watson. Some problems in the theory of numbers. PhD thesis, University of London, 1953. G. L. Watson. Some problems in the theory of numbers. PhD thesis, University of London, 1953.
16.
go back to reference G. L. Watson. Transformations of a quadratic form which do not increase the class-number. Proceedings of the London Mathematical Society, 12:577–587, 1962.MathSciNetMATHCrossRef G. L. Watson. Transformations of a quadratic form which do not increase the class-number. Proceedings of the London Mathematical Society, 12:577–587, 1962.MathSciNetMATHCrossRef
17.
Metadata
Title
Integral Positive Ternary Quadratic Forms
Author
William C. Jagy
Copyright Year
2013
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-7488-3_6

Premium Partner