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"Elliptic function", Encyclopedia of Mathematics, EMS Press, 2001 [1994] MAA, Translation of Abel's paper on elliptic functions. Elliptic Functions and Elliptic Integrals on YouTube , lecture by William A. Schwalm (4 hours)
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, ...
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, ... The zeta function of an elliptic curve over a finite field F p is, ...
In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions. This function is of great importance in the description of the elliptic functions, especially in the description of the modular identity of the Jacobi theta function, the Hermite elliptic transcendents and the Weber modular functions, that are used for ...
In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass . This class of functions is also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p .
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.
For example, the j-invariant j(z) of an elliptic curve, regarded as a function on the set of all elliptic curves, is a modular function. More conceptually, modular functions can be thought of as functions on the moduli space of isomorphism classes of complex elliptic curves.
In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. [1] Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice.