Theta vocabulary II. Multidimensional case

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Abstract

It is shown that the Jacobi and Riemann identities of degree four for the multidimensional theta functions as well as the Weierstrass identities emerge as algebraic consequences of the fundamental multidimensional binary identities connecting the theta functions with Riemann matrices \(\tau\) and \(2\tau\).

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Theta functions and non-linear equations

B A Dubrovin (1981)

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Theta vocabulary I

A. Zabrodin, S. Kharchev (2014)

This paper is an annotated list of transformation properties and identities satisfied by the four theta functions \(\theta _1\), \(\theta _2\), \(\theta _3\), In this paper, we study the decay rl possible 3, 4 and 5-term identCauchy problem for the one-dimensional viscous conservation law where the far fieldar 3-term identities connecting the theta-functions with modular parameters \(\tau\) and \(2\tau\).