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Zapiski Nauchnykh Seminarov LOMI, 1978, Volume 76, Pages 210–215
(Mi znsl1939)
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Siegel's formula for genus 2
O. M. Fomenko
Abstract:
Let $S$ be a semi-integral, symmetric, positive-definite $m\times m$ matrix; $m\geqslant n\geqslant1$. By the Siegel fundamental formula we mean the identity between the Siegel theta series of genus $n$, associated with the genus of the matrix $S$, and the correspond ing Eisenstein-Siegel series (C. L. Siegel, Lectures on the Analytical Theory of Quadratic Forms, 3rd rev. edition, Peppmüller, Göttingen, 1963). The validity of the mentioned formula for $m/2\leqslant n+1$ is an open problem in the general case. In this paper we prove Siegel's formula for $n=2$, $m=6$.
Citation:
O. M. Fomenko, “Siegel's formula for genus 2”, Analytical theory of numbers and theory of functions, Zap. Nauchn. Sem. LOMI, 76, "Nauka", Leningrad. Otdel., Leningrad, 1978, 210–215; J. Soviet Math., 18:3 (1982), 435–439
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https://www.mathnet.ru/eng/znsl1939 https://www.mathnet.ru/eng/znsl/v76/p210
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Abstract page: | 187 | Full-text PDF : | 53 |
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