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Elliptic curve primality proving, abbreviated ECPP, is class of algorithms that provide certificates of primality using sophisticated results from the theory of elliptic ...

Let the elliptic modulus k satisfy 0<k^2<1, and the Jacobi amplitude be given by phi=amu with -pi/2<phi<pi/2. The incomplete elliptic integral of the first kind is then ...

Let the elliptic modulus k satisfy 0<k^2<1. (This may also be written in terms of the parameter m=k^2 or modular angle alpha=sin^(-1)k.) The incomplete elliptic integral of ...

The elliptic lambda function lambda(tau) is a lambda-modular function defined on the upper half-plane by lambda(tau)=(theta_2^4(0,q))/(theta_3^4(0,q)), (1) where tau is the ...

The Engel expansion, also called the Egyptian product, of a positive real number x is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

A self-intersecting minimal surface which can be generated using the Enneper-Weierstrass parameterization with f(z) = 1 (1) g(z) = zeta. (2) Letting z=re^(iphi) and taking ...

The path traced out by a point P on the edge of a circle of radius b rolling on the outside of a circle of radius a. An epicycloid is therefore an epitrochoid with h=b. ...

The Epstein zeta function for a n×n matrix S of a positive definite real quadratic form and rho a complex variable with R[rho]>n/2 (where R[z] denotes the real part) is ...

The terms of equational logic are built up from variables and constants using function symbols (or operations). Identities (equalities) of the form s=t, (1) where s and t are ...

A sequence of real numbers {x_n} is equidistributed on an interval [a,b] if the probability of finding x_n in any subinterval is proportional to the subinterval length. The ...