Representations of integral quadratic forms over dyadic local fields
Author:
Constantin N. Beli
Journal:
Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 100-112
MSC (2000):
Primary 11E08
DOI:
https://doi.org/10.1090/S1079-6762-06-00165-X
Published electronically:
August 10, 2006
MathSciNet review:
2237274
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Abstract: In this paper we give necessary and sufficient conditions for the representations of quadratic lattices over arbitrary dyadic fields. Our result is given in terms of Bases of Norm Generators (BONGs, for short). However, they can be translated in terms of the more traditional Jordan decompositions.
- Constantin N. Beli, Integral spinor norm groups over dyadic local fields, J. Number Theory 102 (2003), no. 1, 125–182. MR 1994477, DOI https://doi.org/10.1016/S0022-314X%2803%2900057-X
[B1]b1 C. N. Beli, BONG version of O’Meara’s Theorem 93:28, preprint.
[B2]b2 C. N. Beli, Representations of quadratic lattices over dyadic local fields, preprint.
- O. T. O’Meara, Introduction to quadratic forms, Die Grundlehren der mathematischen Wissenschaften, Bd. 117, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0152507
- O. T. O’Meara, The integral representations of quadratic forms over local fields, Amer. J. Math. 80 (1958), 843–878. MR 98064, DOI https://doi.org/10.2307/2372837
- Carl Riehm, On the integral representations of quadratic forms over local fields, Amer. J. Math. 86 (1964), 25–62. MR 161853, DOI https://doi.org/10.2307/2373034
[B]b C. N. Beli, Integral spinor norms over dyadic local fields, J. Number Theory 102 (2003), 125–182.
[B1]b1 C. N. Beli, BONG version of O’Meara’s Theorem 93:28, preprint.
[B2]b2 C. N. Beli, Representations of quadratic lattices over dyadic local fields, preprint.
[OM]om O. T. O’Meara, Introduction to quadratic forms, Springer-Verlag, Berlin, 1963.
[OM1]om1 O. T. O’Meara, The integral representation of quadratic forms over local fields, Amer. J. Math. 80 (1958), 843–878.
[R]r C. Riehm, On the integral representations of quadratic forms over local fields, Amer. J. Math. 86 (1964), 25–62.
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Additional Information
Constantin N. Beli
Affiliation:
Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Grivitei Street, 010702-Bucharest, Sector 1, Romania
MR Author ID:
718695
Email:
raspopitu1@yahoo.com
Keywords:
Integral quadratic forms,
dyadic local fields
Received by editor(s):
January 23, 2006
Published electronically:
August 10, 2006
Communicated by:
Brian Conrey
Article copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.