Theta function identities from optical neural network transformations

Abstract

We take a new approach to the generation of Jacobi theta function identities. It is complementary to the procedure which makes use of the evaluation of Parseval-like identities for elementary cylindrically-symmetric functions on computer holograms. Our method is more simple and explicit than this one, which was an outcome of the construction of neurocomputer architectures through the Heisenberg model.

Keywords

• Jacobi theta functions
• Riemann zeta functions
• neural networks
• computer holograms.