Category: Theta functions

Theta divisor
In mathematics, the theta divisor Θ is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally polarized) by the zero locus of the asso
Ramanujan theta function
In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi tripl
Oscillator representation
In mathematics, the oscillator representation is a projective unitary representation of the symplectic group, first investigated by Irving Segal, David Shale, and André Weil. A natural extension of th
Metaplectic group
In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction covers more generally the case of an a
Theta characteristic
In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riema
Jacobi theta functions (notational variations)
There are a number of notational systems for the Jacobi theta functions. The notations given in the Wikipedia article define the original function which is equivalent to where and . However, a similar
Schottky problem
In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties.
Theta function
In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann
Quintuple product identity
In mathematics the Watson quintuple product identity is an infinite product identity introduced by Watson and rediscovered by and . It is analogous to the Jacobi triple product identity, and is the Ma
Jacobi form
In mathematics, a Jacobi form is an automorphic form on the Jacobi group, which is the semidirect product of the symplectic group Sp(n;R) and the Heisenberg group . The theory was first systematically
Fay's trisecant identity
In algebraic geometry, Fay's trisecant identity is an identity between theta functions of Riemann surfaces introduced by Fay . Fay's identity holds for theta functions of Jacobians of curves, but not
Q-theta function
In mathematics, the q-theta function (or modified Jacobi theta function) is a type of q-series which is used to define elliptic hypergeometric series. It is given by where one takes 0 ≤ |q| < 1. It ob
Theta representation
In mathematics, the theta representation is a particular representation of the Heisenberg group of quantum mechanics. It gains its name from the fact that the Jacobi theta function is invariant under
Theta function of a lattice
In mathematics, the theta function of a lattice is a function whose coefficients give the number of vectors of a given norm.
Neville theta functions
In mathematics, the Neville theta functions, named after Eric Harold Neville, are defined as follows: where: K(m) is the complete elliptic integral of the first kind, , and is the elliptic nome. Note
Jacobi triple product
In mathematics, the Jacobi triple product is the mathematical identity: for complex numbers x and y, with |x| < 1 and y ≠ 0. It was introduced by Jacobi in his work Fundamenta Nova Theoriae Functionum