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The Hurwitz zeta function zeta(s,a) is a generalization of the Riemann zeta function zeta(s) that is also known as the generalized zeta function. It is classically defined by ...

There are a number of formulas variously known as Hurwitz's formula. The first is zeta(1-s,a)=(Gamma(s))/((2pi)^s)[e^(-piis/2)F(a,s)+e^(piis/2)F(-a,s)], where zeta(z,a) is a ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

Let the residue from Pépin's theorem be R_n=3^((F_n-1)/2) (mod F_n), where F_n is a Fermat number. Selfridge and Hurwitz use R_n (mod 2^(35)-1,2^(36),2^(36)-1). A ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

The Dirichlet beta function is defined by the sum beta(x) = sum_(n=0)^(infty)(-1)^n(2n+1)^(-x) (1) = 2^(-x)Phi(-1,x,1/2), (2) where Phi(z,s,a) is the Lerch transcendent. The ...

A polynomial with real positive coefficients and roots which are either negative or pairwise conjugate with negative real parts.

The Diophantine equation x_1^2+x_2^2+...+x_n^2=ax_1x_2...x_n which has no integer solutions for a>n.

A number with a continued fraction whose terms are the values of one or more polynomials evaluated on consecutive integers and then interleaved. This property is preserved by ...

Determined the possible values of r and n for which there is an identity of the form (x_1^2+...+x_r^2)(y_1^2+...+y_r^2)=z_1^2+...+z_n^2.