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The Schnirelmann density of a set of nonnegative integers is the greatest lower bound of the fractions A(n)/n where A(n) is the number of terms in the set <=n.

The angles S_1=A_1/2 and S_2=A_2/2 obtained from solving sin(x+omega)=2sinomega (1) for x=A_1,A_2, where omega is the Brocard angle. The half-angles A_1 and A_2 are given by ...

The tail of a vector AB^-> is the initial point A, i.e., the point at which the vector originates. The tails of a statistical distribution with probability density function ...

One of a set of numbers defined in terms of an invariant generated by the finite cyclic covering spaces of a knot complement. The torsion numbers for knots up to 9 crossings ...

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

Probability and Statistics

F_mF_(n+1)-F_nF_(m+1)=(-1)^nF_(m-n), where F_n is a Fibonacci number.

An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...