A theta function is a holomorphic function formed by summing an exponential quadratic form over a lattice.
The Jacobi triple product givesEvery factor is nonzero for , and the product converges to a nonzero limit, so has no zero in the upper half-plane.
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The theta function is a special mathematical function often used in various areas of mathematics, including complex analysis, number theory, and mathematical physics. There are several different definitions of theta functions, but the most common ones arise in the context of elliptic functions and modular forms.