Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-02-01T07:57:45.608Z Has data issue: false hasContentIssue false
  • English
  • Français

Rational Points on Linear Subspaces. Representation of an Integer as a Sum of Squares with Accessory Conditions

Published online by Cambridge University Press:  20 November 2018

T. S. Motzkin
T. S. Motzkin*
Affiliation:
University of California, Los Angeles
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The present study was motivated by an investigation of algebraic conjugates in the complex plane (cf. 4 for one of the results) where some of its concepts are extended and applied.

Let F be a flat (linear subspace) in real affine n-space. The points z = (ζ1, . . . , ζn) on F for which the least common denominator of the coordinates ζv is minimum form a grid G, the main grid of F, studied in § 3.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 206 - 213
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Bôcher, M., Higher algebra (New York, 1907, 1947).Google Scholar
2. Dickson, L. E., History of the theory of numbers, Vol. II (Washington, 1920, 1934).Google Scholar
3. Landau, E., Zahlentheorief Vol. I (Leipzig, 1927).Google Scholar
4. Motzkin, T. S., Sur Véquation irréductible zn + a1zn-1 + … + an = 0, n > 1, à coefficients complexes entiers, dont toutes les racines sont sur une droite. Les 11 classes de droites admissibles. C. R. Acad. Sci. Paris, 222 (1945), 221–223.+1,+à+coefficients+complexes+entiers,+dont+toutes+les+racines+sont+sur+une+droite.+Les+11+classes+de+droites+admissibles.+C.+R.+Acad.+Sci.+Paris,+222+(1945),+221–223.>Google Scholar
5. van der Waerden, B. L., Algebraische Géométrie (Berlin, 1939).Google Scholar