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jarowit
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what is the result of Fourier transformation of functional theta [Heaviside] function?
A functional theta function is a type of mathematical function that is used in number theory and mathematical physics. It is a special type of modular form, which is a function that is invariant under certain transformations.
A functional theta function is a more general form of a regular theta function. While a regular theta function is a complex-valued function of a single variable, a functional theta function is a function of multiple variables and can take on values in more general number fields.
Functional theta functions have various applications in mathematics and physics. They are used in the study of elliptic curves, modular forms, and number theory. They also have applications in quantum field theory, string theory, and mathematical finance.
Functional theta functions are a special type of modular form. They are closely related to regular theta functions, which are also modular forms. In fact, a regular theta function can be expressed as a functional theta function with certain parameters.
Yes, there are several open problems related to functional theta functions. One major open problem is the Riemann hypothesis, which states that all non-trivial zeros of the Riemann zeta function lie on the critical line. Another open problem is the conjecture that there exists a functional theta function that corresponds to every modular form.