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The alternating harmonic series is the series sum_(k=1)^infty((-1)^(k-1))/k=ln2, which is the special case eta(1) of the Dirichlet eta function eta(z) and also the x=1 case ...

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

The generalized Riemann hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1/2. Compare with ...

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 number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively ...

An equation derived by Kronecker: where r(n) is the sum of squares function, zeta(z) is the Riemann zeta function, eta(z) is the Dirichlet eta function, Gamma(z) is the gamma ...

Baer's criterion, also known as Baer's test, states that a module M over a unit ring R is injective iff every module homomorphism from an ideal of R to M can be extended to a ...

Also known as the alternating series test. Given a series sum_(n=1)^infty(-1)^(n+1)a_n with a_n>0, if a_n is monotonic decreasing as n->infty and lim_(n->infty)a_n=0, then ...

A point of a function or surface which is a stationary point but not an extremum. An example of a one-dimensional function with a saddle point is f(x)=x^3, which has f^'(x) = ...

The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...