 Theta function of a lattice

The theta function of a lattice is a special type of mathematical function that arises in the context of complex analysis, number theory, and mathematical physics. Specifically, it is related to the theory of elliptic functions, modular forms, and can be used in various applications including statistical mechanics and string theory. A lattice in this context is typically defined as a discrete subgroup of the complex plane generated by two linearly independent complex numbers \( \omega_1 \) and \( \omega_2 \).