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This article is cited in 4 scientific papers (total in 4 papers)
Embedding $p$-elementary lattices
V. G. Zhuravlev
Vladimir State Pedagogical University
Abstract:
We investigate the ramification of embeddings of local lattices or quadratic forms over the
ring $\mathbb Z_p$ of $p$-adic numbers. It is proved that every primitive embedding decomposes uniquely into an orthogonal sum of minimal indecomposable embeddings, and all such embeddings are constructed for $p$-elementary lattices. Ramification theory enables us to find the number of orbits of representations for forms and, in particular, for numbers by other quadratic forms over $\mathbb Z_p$, and to calculate the local multipliers in the weight formula for representations of a form by a genus of quadratic forms.
DOI:
https://doi.org/10.4213/im229
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Izvestiya: Mathematics, 1999, 63:1, 73–102
Bibliographic databases:
   
MSC: 11E20, 11E25, 11E08, 11H55
Received: 20.07.1997
Citation:
V. G. Zhuravlev, “Embedding $p$-elementary lattices”, Izv. RAN. Ser. Mat., 63:1 (1999), 77–106; Izv. Math., 63:1 (1999), 73–102
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/izv229https://doi.org/10.4213/im229 http://mi.mathnet.ru/eng/izv/v63/i1/p77
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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V. G. Zhuravlev, “Deformations of quadratic Diophantine systems”, Izv. Math., 65:6 (2001), 1085–1126
 -
Budarina N., “On Primitively Universal Quadratic Forms”, Lith. Math. J., 50:2 (2010), 140–163
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N. V. Budarina, “On primitively 2-universal quadratic forms”, St. Petersburg Math. J., 23:3 (2012), 435–458
 -
Budarina N., “Diophantine Properties of the Sequences of Prime Numbers”, Funct. Approx. Comment. Math., 58:2 (2018), 269–279
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