Representations of a \(p\)-elementary form by a genus. (English. Russian original) Zbl 1130.11313

Fedorova, S. V.

J. Math. Sci., New York 118, No. 1, 4895-4903 (2003); translation from Zap. Nauchn. Semin. POMI 276, 276-290 (2001).

Summary: 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.

MSC:

11E25	Sums of squares and representations by other particular quadratic forms
11E08	Quadratic forms over local rings and fields