Small zeros of quadratic forms over algebraic function fields

Albrecht Pfister

Acta Arithmetica (1997)

  • Volume: 79, Issue: 3, page 221-238
  • ISSN: 0065-1036

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Albrecht Pfister. "Small zeros of quadratic forms over algebraic function fields." Acta Arithmetica 79.3 (1997): 221-238. <http://eudml.org/doc/206977>.

@article{AlbrechtPfister1997,
author = {Albrecht Pfister},
journal = {Acta Arithmetica},
keywords = {Riemann-Roch theorem; quadratic form; algebraic function field; smallest degree of the pole divisors},
language = {eng},
number = {3},
pages = {221-238},
title = {Small zeros of quadratic forms over algebraic function fields},
url = {http://eudml.org/doc/206977},
volume = {79},
year = {1997},
}

TY - JOUR
AU - Albrecht Pfister
TI - Small zeros of quadratic forms over algebraic function fields
JO - Acta Arithmetica
PY - 1997
VL - 79
IS - 3
SP - 221
EP - 238
LA - eng
KW - Riemann-Roch theorem; quadratic form; algebraic function field; smallest degree of the pole divisors
UR - http://eudml.org/doc/206977
ER -

References

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  1. [1] J. W. S. Cassels, Bounds for the least solutions of homogeneous quadratic equations, Proc. Cambridge Philos. Soc. 51 (1955), 262-264. Addendum, Proc. Cambridge Philos. Soc. 52 (1956), 604. Zbl0064.28302
  2. [2] J. W. S. Cassels, On the representation of rational functions as sums of squares, Acta Arith. 9 (1964), 79-82. Zbl0131.25001
  3. [3] J. W. S. Cassels, Rational Quadratic Forms, London Math. Soc. Monographs 13, Academic Press, London, 1978. 
  4. [4] A. Pfister, Quadratic Forms with Applications to Algebraic Geometry and Topology, London Math. Soc. Lecture Note Ser. 217, Cambridge Univ. Press, 1995. Zbl0847.11014
  5. [5] A. Prestel, On the size of zeros of quadratic forms over rational function fields, J. Reine Angew. Math. 378 (1987), 101-112. Zbl0606.10014
  6. [6] S. Raghavan, Bounds for minimal solutions of Diophantine equations, Nachr. Akad. Wiss. Göttingen 1975 (9), 109-114. Zbl0317.10025
  7. [7] P. Roquette, Analytic theory of elliptic functions over local fields, Hamburg. Math. Einzelschr. 1, Vandenhoeck & Ruprecht, Göttingen, 1970. Zbl0194.52002
  8. [8] H. P. Schlickewei and W. M. Schmidt, Quadratic forms which have only large zeros, Monatsh. Math. 105 (1988), 295-311. Zbl0684.10016

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