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Siegel theta series : ウィキペディア英語版
Siegel theta series

In mathematics, a Siegel theta series is a Siegel modular form associated to a positive definite lattice, generalizing the 1-variable theta function of a lattice.
==Definition==

Suppose that ''L'' is a positive definite lattice. The Siegel theta series of degree ''g'' is defined by
:\Theta_L^g(T) = \sum_\exp(\pi i Tr(\lambda T \lambda^t))
where ''T'' is an element of the Siegel upper half plane of degree ''g''.
This is a Siegel modular form of degree ''d'' and weight dim(''L'')/2 for some subgroup of the Siegel modular group. If the lattice ''L'' is even and unimodular then this is a Siegel modular form for the full Siegel modular group.
When the degree is 1 this is just the usual theta function of a lattice.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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