Geodesic
Number of representations of local $p$-one-dimensional forms by the genus
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 334-348 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study branching of representations of a locally $p$-one-dimensional form by a genus of positive definite integral quadratic forms. We give a complete list of minimal representations by a genus for forms of square level. Gauss–Minkowski formulas are obtained for heights of representations over the ring of integers. As an application, we obtain formulas for heights of primitive representations by genera for specific forms constructed by the method of orthogonal complement. 
@article{ZNSL_2001_276_a16,
     author = {A. V. Khorosheva},
     title = {Number of representations of local $p$-one-dimensional forms by the genus},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {334--348},
     year = {2001},
     volume = {276},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a16/}
}
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A. V. Khorosheva. Number of representations of local $p$-one-dimensional forms by the genus. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 334-348. http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a16/