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On primitively 2-universal quadratic forms


Author: N. V. Budarina
Translated by: N. B. Lebedinskaya
Original publication: Algebra i Analiz, tom 23 (2011), nomer 3.
Journal: St. Petersburg Math. J. 23 (2012), 435-458
MSC (2010): Primary 11E08
Published electronically: March 2, 2012
MathSciNet review: 2896164
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Abstract: The primitive representations of binary positive definite, classically integral quadratic forms over the local rings $ \mathbb{Z}_p$ are studied. For the global ring, an efficient method is obtained for determining when a quadratic form is primitively 2-universal.


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Additional Information

N. V. Budarina
Affiliation: Khabarovsk Division, Institute of Applied Mathematics, Russian Academy of Sciences, 54 Dzerzhinsky Street, Khabarovsk 680000, Russia
Email: buda77@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-2012-01203-3
Keywords: Primitively universal quadratic forms, $p$-adic symbols
Received by editor(s): February 5, 2010
Published electronically: March 2, 2012
Additional Notes: Supported by RFBR (grants nos. 08-01-00326 and 07-01-00306)
Article copyright: © Copyright 2012 American Mathematical Society