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)...

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...

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...

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

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...

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...

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...

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...

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 ) ∈...

matrix is a generator matrix for the Barnes–Wall lattice B W 16 {\displaystyle BW_{16}} . The lattice theta function for the Barnes Wall lattice B W 16 {\displaystyle...

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...

applied in the theory of theta functions and is a possible method in geometry of numbers. In fact in more recent work on counting lattice points in regions...

scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation...

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...

umbral moonshine is a mysterious connection between Niemeier lattices and Ramanujan's mock theta functions. It is a generalization of the Mathieu moonshine...

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...

science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems...

Every elliptic function with respect to a given period lattice Λ {\displaystyle \Lambda } can be expressed as a rational function in terms of ℘ {\displaystyle...

periodic function can be constructed with little effort. For example, assume that the periods are 1 and i, so that the repeating lattice is the set of unit...

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

of the lattice constant, which is to be viewed as an adjustable parameter. The quasi-harmonic approximation expands upon the harmonic phonon model of...

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...

e^{i\left(\theta _{i,j}^{x}+\theta _{i+1,j}^{y}-\theta _{i,j+1}^{x}\right)}=|i,j\rangle e^{i\left(\theta _{i,j}^{x}+\theta _{i+1,j}^{y}-\theta _{i,j+1}^{x}-\theta...

The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy-Pomeau-Pazzis and Frisch-Hasslacher-Pomeau models), is...

"prove" them Umbral moonshine, a mysterious connection between Niemeier lattices and Ramanujan's mock theta functions Francisco Umbral (1932–2007), Spanish...

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...

on a lattice Solutions to the Schrödinger equation in spherical and cylindrical coordinates for a free particle Position space representation of the...

} The branch points of j are at {0, 1, ∞}, so that j is a Belyi function. Define the nome q = eπiτ and the Jacobi theta function, ϑ ( 0 ; τ ) = ϑ 00 (...

perturbation. NB: The concept of quasiperiodic function, for example the sense in which theta functions and the Weierstrass zeta function in complex analysis are...