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In mathematics, the theta function of a lattice is a function whose coefficients give the number of vectors of a given norm. One can associate to any (positive-definite)...

In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces...

properties of the E8 lattice and its 24-dimensional cousin, the Leech lattice. One can associate to any (positive-definite) lattice Λ a theta function given...

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...

zone of that lattice. For example, the sinc function for the hexagonal lattice is a function whose Fourier transform is the indicator function of the unit...

variables. Theta function may also refer to: q-theta function, θ ( z ; q ) {\displaystyle \theta (z;q)} , a type of q-series Theta function of a lattice, Θ Λ...

a Siegel theta series is a Siegel modular form associated to a positive definite lattice, generalizing the 1-variable theta function of a lattice. Suppose...

the theta constants are Siegel modular forms. The theta function of a lattice is essentially a special case of a theta constant. The theta function θm(τ...

mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight...

summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic behaviour of the Riemann...

Theta functions of even unimodular lattices An even unimodular lattice L in Rn is a lattice generated by n vectors forming the columns of a matrix of...

that a plane wave (of any type) is incident on planes of lattice points, with separation d {\displaystyle d} , at an angle θ {\displaystyle \theta } as...

Bloch's theorem a statement about lattice periodicity, in this proof all the symmetries are encoded as translation symmetries of the wave function itself. Proof...

statistical mechanics, the two-dimensional square lattice Ising model is a simple lattice model of interacting magnetic spins. The model is notable for...

[reciprocal lattice] × {\displaystyle \times } [structure factor] ∗ {\displaystyle \ast } [ sinc function]. Thus the intensity, which is a delta function of position...

elliptic curves and they generate the field of elliptic functions with respect to a given period lattice. A cubic of the form C g 2 , g 3 C = { ( x , y ) ∈...

not the derivative of a 0-form (that is, a function): the angle θ {\displaystyle \theta } is not a globally defined smooth function on the entire punctured...

generally has a density around 63.5%. A lattice arrangement (commonly called a regular arrangement) is one in which the centers of the spheres form a very symmetric...

density function for the separation Δ x {\displaystyle \Delta x} of a pair of planes, m {\displaystyle m} lattice spacings apart. For the separation of neighbouring...

plane of the argument u {\displaystyle u} , the twelve functions form a repeating lattice of simple poles and zeroes. Depending on the function, one repeating...