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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 1, Pages 77–106 (Mi izv229)  

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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English version:
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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\pages 73--102
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Zhuravlev, “Deformations of quadratic Diophantine systems”, Izv. Math., 65:6 (2001), 1085–1126  mathnet  crossref  crossref  mathscinet  zmath
    2. Budarina N., “On Primitively Universal Quadratic Forms”, Lith. Math. J., 50:2 (2010), 140–163  crossref  mathscinet  zmath  isi  scopus
    3. N. V. Budarina, “On primitively 2-universal quadratic forms”, St. Petersburg Math. J., 23:3 (2012), 435–458  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    4. Budarina N., “Diophantine Properties of the Sequences of Prime Numbers”, Funct. Approx. Comment. Math., 58:2 (2018), 269–279  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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