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Let pi_(m,n)(x) denote the number of primes <=x which are congruent to n modulo m (i.e., the modular prime counting function). Then one might expect that ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

An even Mathieu function ce_r(z,q) with characteristic value a_r.

A mathematical relationship transforming a function f(x) to the form f(x+a).

Wirsing (1974) showed, among other results, that if F_n(x) is the Gauss-Kuzmin distribution, then lim_(n->infty)(F_n(x)-lg(1+x))/((-lambda)^n)=Psi(x), (1) where ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of ...

Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...