Geodesic
Representations of $p$-elementary form by the genus
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 276-290 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the branching of representations of a $p$-elementary quadratic form by a genus of positive definite locally $p$-two-dimensional forms. A primitive representation of a $p$-elementary form is decomposed into a direct sum of minimal indecomposable representations; the latter representations are found in an explicit form. For the case of branching, we find local multipliers of the weight of representations of a form by a genus. As an application, we calculate the number of embeddings into the classical root lattices. The method of orthogonal complement is applied in constructing new genera of quadratic forms. 
@article{ZNSL_2001_276_a12,
     author = {S. V. Fedorova},
     title = {Representations of $p$-elementary form by the genus},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {276--290},
     year = {2001},
     volume = {276},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a12/}
}
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S. V. Fedorova. Representations of $p$-elementary form by the genus. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 276-290. http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a12/