Theta vocabulary II. Multidimensional case

TL;DR

This paper demonstrates that classical identities for multidimensional theta functions, such as Jacobi, Riemann, and Weierstrass identities, can be derived from fundamental binary identities involving Riemann matrices.

Contribution

It reveals that key identities of multidimensional theta functions are algebraic consequences of fundamental binary identities, unifying their derivation.

Findings

Jacobi and Riemann identities follow from binary identities

Weierstrass identities are algebraic consequences of fundamental identities

Connections between theta functions and Riemann matrices are clarified

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 $2\tau$.