Theta function

In mathematics, theta functions are special functions of several complex variables. They are important in several areas, including the theories of abelian varieties and moduli spaces, and of quadratic forms. They have also been applied to soliton theory. When generalized to a Grassmann algebra, they also appear in quantum field theory, specifically string theory and D-branes.

Related Topics:
Mathematics - Special function - Several complex variables - Abelian varieties - Moduli space - Quadratic form - Soliton - Grassmann algebra - Quantum field theory - String theory - D-brane

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The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions (sometimes called quasi-periodicity, though this is not related to the use of that term for dynamical systems). In the abstract theory this is shown to come from a line bundle condition of descent.

Related Topics:
Elliptic function - Dynamical system - Line bundle - Descent

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