mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used...

an elliptic filter will coincide with the poles of the elliptic rational function, which are derived in the article on elliptic rational functions. The...

analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because...

In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied...

Weierstrass's elliptic functions Lemniscate elliptic functions Theta functions Neville theta functions Modular lambda function Closely related are the...

follows naturally from a curious property of Weierstrass's elliptic functions. These functions and their first derivative are related by the formula ℘ ′...

Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions is also...

In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied...

number field K, the Hasse–Weil zeta function is conjecturally related to the group of rational points of the elliptic curve over K by the Birch and Swinnerton-Dyer...

upper half space. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables...

Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number...

numerators and denominators for constructing all the rational functions which are really functions on the underlying projective space P(V). One might ask...

the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve E {\displaystyle E} defined over the field of rational numbers or more...

In number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way...

Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional...

field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic...

In mathematics, an elliptic hypergeometric series is a series Σcn such that the ratio cn/cn−1 is an elliptic function of n, analogous to generalized hypergeometric...

constant. The elliptic functions are such functions. ("Incommensurate" in this context means not real multiples of each other.) Periodic functions can take...

is known, at least when A is an elliptic curve. The question of the rank is thought to be bound up with L-functions (see below). The torsor theory here...

particular the subfield of algebraic geometry, a rational map or rational mapping is a kind of partial function between algebraic varieties. This article uses...

modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting. A polynomial function is one that has...

polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x1/n). All elementary functions are continuous...

applies to an elliptic curve E, and the problem it attempts to solve is the prediction of the rank of the elliptic curve over the rational numbers (or another...

filter is named after Wilhelm Cauer and the transfer function is based on elliptic rational functions. Cauer-type filters use generalized continued fractions...

In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic...

Hasse's theorem on elliptic curves, also referred to as the Hasse bound, provides an estimate of the number of points on an elliptic curve over a finite...

)}=0,\quad j(i)=1728=12^{3}.} Rational functions of j {\displaystyle j} are modular, and in fact give all modular functions of weight 0. Classically, the...

the lemniscate leads to elliptic integrals, as was discovered in the eighteenth century. Around 1800, the elliptic functions inverting those integrals...

conjectures, formulated for general classes of L-functions (the very general setting being for L-functions associated to Chow motives over number fields)...

asserts that every elliptic curve defined over the rational numbers is modular. In the 1950s and 1960s a connection between elliptic curves and modular...