Effective version of Tartakowsky's Theorem

J. S. Hsia; M. I. Icaza

Acta Arithmetica (1999)

  • Volume: 89, Issue: 3, page 235-253
  • ISSN: 0065-1036

How to cite

top

J. S. Hsia, and M. I. Icaza. "Effective version of Tartakowsky's Theorem." Acta Arithmetica 89.3 (1999): 235-253. <http://eudml.org/doc/207267>.

@article{J1999,
author = {J. S. Hsia, M. I. Icaza},
journal = {Acta Arithmetica},
keywords = {-adic representations; representation of integers; integral quadratic forms; JFM 56.0882.04; integral quadratic lattices; ring of integers},
language = {eng},
number = {3},
pages = {235-253},
title = {Effective version of Tartakowsky's Theorem},
url = {http://eudml.org/doc/207267},
volume = {89},
year = {1999},
}

TY - JOUR
AU - J. S. Hsia
AU - M. I. Icaza
TI - Effective version of Tartakowsky's Theorem
JO - Acta Arithmetica
PY - 1999
VL - 89
IS - 3
SP - 235
EP - 253
LA - eng
KW - -adic representations; representation of integers; integral quadratic forms; JFM 56.0882.04; integral quadratic lattices; ring of integers
UR - http://eudml.org/doc/207267
ER -

References

top
  1. [BI] R. Baeza and M. I. Icaza, Decomposition of positive definite integral quadratic forms as sums of positive definite quadratic forms, in: Proc. Sympos. Pure Math. 58, Amer. Math. Soc., 1995, 63-72. Zbl0820.11024
  2. [BH] J. W. Benham and J. S. Hsia, Spinor equivalence of quadratic forms, J. Number Theory 17 (1983), 337-342. Zbl0532.10012
  3. [C] J. W. S. Cassels, Rational Quadratic Forms, Academic Press, 1978. Zbl0395.10029
  4. [HKK] J. S. Hsia, Y. Kitaoka and M. Kneser, Representations by positive definite quadratic forms, J. Reine Angew. Math. 301 (1978), 132-141. Zbl0374.10013
  5. [Hu] P. Humbert, Réduction de formes quadratiques dans un corps algébrique fini, Comment. Math. Helv. 23 (1949), 50-63. Zbl0034.31102
  6. [Ki1] Y. Kitaoka, Siegel Modular Forms and Representation by Quadratic Forms, Tata Lecture Notes, Springer, 1986. Zbl0596.10020
  7. [Ki2] Y. Kitaoka, A note on representation of positive definite binary quadratic forms by positive definite quadratic forms in 6 variables, Acta Arith. 54 (1990), 317-322. Zbl0705.11018
  8. [Ki3] Y. Kitaoka, Arithmetic of Quadratic Forms, Cambridge Univ. Press, 1993. 
  9. [Kn] M. Kneser, Quadratische Formen, Göttingen Lecture Notes, 1973/74. 
  10. [N] G. L. Nipp, Quaternary Quadratic Forms - Computer Generated Tables, Springer, 1991. Zbl0727.11018
  11. [OM1] O. T. O'Meara, The integral representations of quadratic forms over local rings, Amer. J. Math. 86 (1958), 843-878. 
  12. [OM2] O. T. O'Meara, Introduction to Quadratic Forms, Springer, 1973. 
  13. [T] W. Tartakowsky, Die Gesamtheit der Zahlen, die durch eine positive quadratische Form F ( x ₁ , . . . , x s ) (s ≥ 4) darstellbar sind, Izv. Akad. Nauk SSSR 7 (1929), 111-122, 165-195. Zbl56.0882.04
  14. [W] G. L. Watson, Quadratic diophantine equations, Philos. Trans. Roy. Soc. London Ser. A 253 (1960), 227-254. Zbl0102.28102

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.