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Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

Landau (1911) proved that for any fixed x>1, sum_(0<|I[rho]|<=T)x^rho=-T/(2pi)Lambda(x)+O(lnT) as T->infty, where the sum runs over the nontrivial Riemann zeta function zeros ...

Let F be the set of complex analytic functions f defined on an open region containing the closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each f in ...

Big-omega notation is the inverse of the Landau symbol O, f(n) in O(g(n))<=>g(n) in Omega(f(n)).

Landau's function g(n) is the maximum order of an element in the symmetric group S_n. The value g(n) is given by the largest least common multiple of all partitions of the ...

Landau's problems are the four "unattackable" problems mentioned by Landau in the 1912 Fifth Congress of Mathematicians in Cambridge, namely: 1. The Goldbach conjecture, 2. ...

Let ||f|| be the supremum of |f(x)|, a real-valued function f defined on (0,infty). If f is twice differentiable and both f and f^('') are bounded, Landau (1913) showed that ...

The Landau-Mignotte bound, also known as the Mignotte bound, is used in univariate polynomial factorization to determine the number of Hensel lifting steps needed. It gives ...

Little-omega notation is the inverse of the Landau symbol o, i.e., f(n) in o(phi(n)) <==> phi(n) in omega(f(n)).

Symbols used to identify irreducible representations of groups: A= singly degenerate state which is symmetric with respect to rotation about the principal C_n axis, B= singly ...