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The expected number of real zeros E_n of a random polynomial of degree n if the coefficients are independent and distributed normally is given by E_n = ...

The Riemann-Siegel integral formula is the following representation of the xi-function xi(s) found in Riemann's Nachlass by Bessel-Hagen in 1926 (Siegel 1932; Edwards 2001, ...

The term analysis is used in two ways in mathematics. It describes both the discipline of which calculus is a part and one form of abstract logic theory. Analysis is the ...

The Gauss-Kuzmin distribution is the distribution of occurrences of a positive integer k in the continued fraction of a random (or "generic") real number. Consider xi_n ...

In an additive group G, the additive inverse of an element a is the element a^' such that a+a^'=a^'+a=0, where 0 is the additive identity of G. Usually, the additive inverse ...

An alternating multilinear form on a real vector space V is a multilinear form F:V tensor ... tensor V->R (1) such that ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

A compactum (plural: compacta) is a compact metric space. An example of a compactum is any finite discrete metric space. Also, the space [0,1] union [2,3] is a compactum, ...

An equation of the form y=ax^3+bx^2+cx+d, (1) where two of the roots of the equation coincide (and all three are therefore real), i.e., y = a(x-r_1)^2(x-r_2) (2) = ...

Let f(x) be a positive definite, measurable function on the interval (-infty,infty). Then there exists a monotone increasing, real-valued bounded function alpha(t) such that ...