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The sum c_q(m)=sum_(h^*(q))e^(2piihm/q), (1) where h runs through the residues relatively prime to q, which is important in the representation of numbers by the sums of ...

Spinor fields describing particles of zero rest mass satisfy the so-called zero rest mass equations. Examples of zero rest mass particles include the neutrino (a fermion) and ...

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A ...

The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are ...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

There are at least two distinct notions of an intensity function related to the theory of point processes. In some literature, the intensity lambda of a point process N is ...

A point process N on R is said to be interval stationary if for every r=1,2,3,... and for all integers i_i,...,i_r, the joint distribution of {tau_(i_1+k),...,tau_(i_r+k)} ...

The commutator series of a Lie algebra g, sometimes called the derived series, is the sequence of subalgebras recursively defined by g^(k+1)=[g^k,g^k], (1) with g^0=g. The ...

The Littlewood conjecture states that for any two real numbers x,y in R, lim inf_(n->infty)n|nx-nint(nx)||ny-nint(ny)|=0 where nint(z) denotes the nearest integer function. ...