Theta function
Theta The"ta, n. [L., fr. Gr. qh^ta, the Greek letter [theta], [Theta].] A letter of the Greek alphabet corresponding to th in English; -- sometimes called the unlucky letter, from being used by the judges on their ballots in passing condemnation on a prisoner, it being the first letter of the Greek qa`natos, death. [1913 Webster]

{Theta function} (Math.), one of a group of functions used in developing the properties of elliptic functions. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • Theta function — heta 1 with u = i pi z and with nome q = e^{i pi au}= 0.1 e^{0.1 i pi}. Conventions are (mathematica): heta 1(u;q) = 2 q^{1/4} sum {n=0}^infty ( 1)^n q^{n(n+1)} sin((2n+1)u) this is: heta 1(u;q) = sum {n= infty}^{n=infty} ( 1)^{n 1/2}… …   Wikipedia

  • 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. Definition One can associate to any (positive definite) lattice Λ a theta function given by The theta function of a… …   Wikipedia

  • Riemann-Siegel theta function — In mathematics, the Riemann Siegel theta function is defined in terms of the Gamma function as: heta(t) = arg left(Gammaleft(frac{2it+1}{4} ight) ight) frac{log pi}{2} tfor real values of t. Here the argument is chosen in such a way that a… …   Wikipedia

  • Ramanujan theta function — In mathematics, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in terms of the… …   Wikipedia

  • Q-theta function — In mathematics, the q theta function is a type of q series. It is given by: heta(z;q)=prod {n=0}^infty (1 q^nz)(1 q^{n+1}/z)where one takes 0le|q| …   Wikipedia

  • Theta — The ta, n. [L., fr. Gr. qh^ta, the Greek letter [theta], [Theta].] A letter of the Greek alphabet corresponding to th in English; sometimes called the unlucky letter, from being used by the judges on their ballots in passing condemnation on a… …   The Collaborative International Dictionary of English

  • 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 the action of a discrete subgroup of the… …   Wikipedia

  • 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 Riemann surface, it is therefore L such that L 2 is …   Wikipedia

  • Theta-divisor — In mathematics, the theta divisor Theta; 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 associated Riemann theta function. It is… …   Wikipedia

  • Theta — (uppercase Θ, lowercase θ or IPA|ϑ; el. Θήτα) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth. In the system of Greek numerals it has a value of 9. In Classical Greek θ represented an aspirated voiceless dental …   Wikipedia

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