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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 ...

The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...

Let p be an odd prime and F_n the cyclotomic field of p^(n+1)th roots of unity over the rational field. Now let p^(e(n)) be the power of p which divides the class number h_n ...

A rewriting of a given quantity (e.g., a matrix) in terms of a combination of "simpler" quantities.

A multiplication * is said to be right distributive if (x+y)z=xz+yz for every x, y, and z. Similarly, it is said to be left distributive if z(x+y)=zx+zy for every x, y, and ...

For discrete problems in which no efficient solution method is known, it might be necessary to test each possibility sequentially in order to determine if it is the solution. ...

A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.

Lehmer's formula is a formula for the prime counting function, pi(x) = (1) where |_x_| is the floor function, a = pi(x^(1/4)) (2) b = pi(x^(1/2)) (3) b_i = pi(sqrt(x/p_i)) ...

The second-order ordinary differential equation y^('')-[(m(m+1)+1/4-(m+1/2)cosx)/(sin^2x)+(lambda+1/2)]y=0.

A positive integer n is kth powerfree if there is no number d such that d^k|n (d^k divides n), i.e., there are no kth powers or higher in the prime factorization of n. A ...