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A cyclotomic field Q(zeta) is obtained by adjoining a primitive root of unity zeta, say zeta^n=1, to the rational numbers Q. Since zeta is primitive, zeta^k is also an nth ...

A series suma(n)e^(-lambda(n)z), where a(n) and z are complex and {lambda(n)} is a monotonic increasing sequence of real numbers. The numbers lambda(n) are called the ...

For any alpha in A (where A denotes the set of algebraic numbers), let |alpha|^_ denote the maximum of moduli of all conjugates of alpha. Then a function ...

A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

An elliptic cylinder is a cylinder with an elliptical cross section. The elliptic cylinder is a quadratic ruled surface. The parametric equations for the laterals sides of an ...

The Erdős-Selfridge function g(k) is defined as the least integer bigger than k+1 such that the least prime factor of (g(k); k) exceeds k, where (n; k) is the binomial ...

A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

Because the Legendre polynomials form a complete orthogonal system over the interval [-1,1] with respect to the weighting function w(x)=1, any function f(x) may be expanded ...

Any symmetric polynomial (respectively, symmetric rational function) can be expressed as a polynomial (respectively, rational function) in the elementary symmetric ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...