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arXiv · 1502.04603

Theta vocabulary I

S. Kharchev·A. Zabrodin
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Abstract

This paper is an annotated list of transformation properties and identities satisfied by the four theta functions $\theta _1$, $\theta _2$, $\theta _3$, $\theta _4$ 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 $\tau$ and $2\tau$.

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S. Kharchev, A. Zabrodin. 2014-11-25. Theta vocabulary I. https://doi.org/10.1016/j.geomphys.2015.03.010

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