Theta vocabulary I
Theta vocabulary I
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DOI：
10.1016/j.geomphys.2015.03.010
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发表时间：
2014-11
影响因子：
1.5
通讯作者：
S. Kharchev;A. Zabrodin
中科院分区：
文献类型：
--
作者：
S. Kharchev;A. Zabrodin
本文给出了一个复数变量的四个θ函数θ 1， θ 2, θ 3， θ 4所满足的变换性质和恒等式的注释表，并以现成的形式给出。本文试图揭示函数各种恒等式背后的规律。结果表明，所有可能的4次3项、4项和5项恒等式都是连接具有模参数τ和2 τ的函数的6个基本双线性3项恒等式的代数结果。
This paper is an annotated list of transformation properties and identities satisfied by the four theta functions θ 1, θ 2, θ 3, θ 4 of one complex variable, presented in a ready-to-use form. An attempt is made to reveal a pattern behind various identities for the theta-functions. It is shown that all possible 3, 4 and 5-term identities of degree four emerge as algebraic consequences of the six fundamental bilinear 3-term identities connecting the theta-functions with modular parameters τ and 2 τ.