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This article is cited in 2 scientific papers (total in 2 papers)
Duality in Siegel's theorem on representation by a genus of quadratic forms, and the averaging operator
A. N. Andrianov
Abstract:
Let $S$ and $T$ be two integral positive definite quadratic forms in the same number of variables, and let $S_1,\dots,S_H$ and $T_1,\dots,T_h$ be complete systems of representatives of the different classes in the genus of the form $S$ and $~T$, respectively. The author proves, in particular, that
$$
\bigg(\sum_{i=1}^He(S_i)^{-1}\bigg)^{-1}\sum_{i=1}^He(S_i)^{-1}r(S_i,T)=\bigg(\sum_{j=1}^he(T_j)^{-1}\bigg)^{-1}\sum_{j=1}^he(T_j)^{-1}r(S,T_j),
$$
where $r(S',T')$ denotes the number of integral representations of the form $T'$ by the form $S'$, and $e(S') = r(S',S')$.
Bibliography: 6 titles.
Received: 14.04.1983
Citation:
A. N. Andrianov, “Duality in Siegel's theorem on representation by a genus of quadratic forms, and the averaging operator”, Mat. Sb. (N.S.), 122(164):1(9) (1983), 3–11; Math. USSR-Sb., 50:1 (1985), 1–10
Linking options:
https://www.mathnet.ru/eng/sm2269https://doi.org/10.1070/SM1985v050n01ABEH002567 https://www.mathnet.ru/eng/sm/v164/i1/p3
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Abstract page: | 283 | Russian version PDF: | 90 | English version PDF: | 6 | References: | 53 | First page: | 2 |
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