On the distribution of squares of integral quaternions

Gerald Kuba

Acta Arithmetica (2000)

  • Volume: 93, Issue: 4, page 359-372
  • ISSN: 0065-1036

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Gerald Kuba. "On the distribution of squares of integral quaternions." Acta Arithmetica 93.4 (2000): 359-372. <http://eudml.org/doc/207419>.

@article{GeraldKuba2000,
author = {Gerald Kuba},
journal = {Acta Arithmetica},
keywords = {number of distinct squares; integral quaternions; lattice points},
language = {eng},
number = {4},
pages = {359-372},
title = {On the distribution of squares of integral quaternions},
url = {http://eudml.org/doc/207419},
volume = {93},
year = {2000},
}

TY - JOUR
AU - Gerald Kuba
TI - On the distribution of squares of integral quaternions
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 4
SP - 359
EP - 372
LA - eng
KW - number of distinct squares; integral quaternions; lattice points
UR - http://eudml.org/doc/207419
ER -

References

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  1. [1] F. Chamizo and H. Iwaniec, On the sphere problem, Rev. Mat. Iberoamericana 11 (1995), 417-429. Zbl0837.11054
  2. [2] D. R. Heath-Brown, Lattice points in the sphere, in: Number Theory in Progress (Zakopane, 1997), Vol. II, de Gruyter, Berlin, 1999, 883-892. Zbl0929.11040
  3. [3] E. Hlawka, Integrale auf konvexen Körpern, Monatsh. Math. 54 (1950), 1-36. 
  4. [4] A. Hurwitz, Vorlesungen über die Zahlentheorie der Quaternionen, Berlin, 1919. Zbl47.0106.01
  5. [5] M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996. 
  6. [6] E. Krätzel, Lattice Points, Kluwer, Dordrecht, 1988. 
  7. [7] E. Krätzel and W. G. Nowak, Lattice points in large convex bodies II, Acta Arith. 62 (1992), 285-295. Zbl0769.11037
  8. [8] H. Müller und W. G. Nowak, Potenzen von Gaußschen ganzen Zahlen in Quadraten, Mitt. Math. Ges. Hamburg 18 (1999), 119-126. 
  9. [9] I. M. Vinogradov, On the number of integral points in a three-dimensional domain, in: Selected Works, Berlin, 1985, 304-324. 

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