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Dini's theorem is a result in real analysis relating pointwise convergence of sequences of functions to uniform convergence on a closed interval. For an increasing sequence ...

A generalization of Fermat's little theorem. Euler published a proof of the following more general theorem in 1736. Let phi(n) denote the totient function. Then a^(phi(n))=1 ...

Let sigma(n) be the divisor function. Then lim sup_(n->infty)(sigma(n))/(nlnlnn)=e^gamma, where gamma is the Euler-Mascheroni constant. Ramanujan independently discovered a ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

A real-valued function g defined on a convex subset C subset R^n is said to be quasi-concave if for all real alpha in R, the set {x in C:g(x)>=alpha} is convex. This is ...

A real-valued function g defined on a convex subset C subset R^n is said to be quasi-convex if for all real alpha in R, the set {x in C:g(x)<alpha} is convex. This is ...

A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

The definition of an Anosov map is the same as for an Anosov diffeomorphism except that instead of being a diffeomorphism, it is a map. In particular, an Anosov map is a C^1 ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then every even function h(rho) analytic in ...