Theta function of a lattice
Introduction In mathematics, the '''theta function of a lattice''' is a function whose coefficients give the number of vectors of a given norm.
Definition One can associate to any (positive-definite) lattice Λ a theta function given by:The theta function of a lattice is then a holomorphic function on the upper half-plane. Furthermore, the theta function of an even unimodular lattice of rank ''n'' is actually a modular form of weight ''n''/2.The theta function of an integral lattice is often written as a power series in  so that the coefficient of ''q''''n'' gives the number of lattice vectors of norm 2''n''.
See also * Theta constant
References *