Explore: Theta Series

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

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

weak Maass form, and a mock theta function is essentially a mock modular form of weight ⁠1/2⁠. The first examples of mock theta functions were described

for the full modular group PSL(2,Z). The theta function of an integral lattice is often written as a power series in q = e 2 i π τ {\displaystyle q=e^{2i\pi

Theta (UK: /ˈθiːtə/ , US: /ˈθeɪtə/) uppercase Θ or ϴ; lowercase θ or ϑ; Ancient Greek: θῆτα thē̂ta [tʰɛ̂ːta]; Modern: θήτα thī́ta [ˈθita]) is the eighth

André Weil's representation theoretical formulation of the theory of theta series in Weil (1964). The Shimura correspondence as constructed by Jean-Loup

\sin \theta =\theta -{\frac {\theta ^{3}}{3!}}+{\frac {\theta ^{5}}{5!}}-{\frac {\theta ^{7}}{7!}}+\quad \cdots } which is the infinite power series expansion

In number theory, a Poincaré series is a mathematical series generalizing the classical theta series that is associated to any discrete group of symmetries

matrix is a computational way of describing the Hecke operator action on theta series as modular forms. The theory was developed in part by Brandt's student

_{k=1}^{\infty }{\frac {\cos(k\theta )}{k}}=-{\frac {1}{2}}\ln(2-2\cos \theta )=-\ln \left(2\sin {\frac {\theta }{2}}\right),0<\theta <2\pi } ∑ k = 1 ∞ sin ⁡