Dedekind eta function information

In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane...

eta function may refer to: The Dirichlet eta function η(s), a Dirichlet series The Dedekind eta function η(τ), a modular form The Weierstrass eta function...

n − 1 , {\displaystyle \tau =n{\sqrt {-1}},} and Dedekind eta function η ( τ ) . {\displaystyle \eta (\tau ).} Then for n = 1 , 2 , 3 , … {\displaystyle...

(q)^{24}=\eta (z)^{24}=\Delta (z),} where q = exp(2πiz) with Im z > 0, ϕ {\displaystyle \phi } is the Euler function, η is the Dedekind eta function, and the...

theory, Dedekind function can refer to any of three functions, all introduced by Richard Dedekind Dedekind eta function Dedekind psi function Dedekind zeta...

of the Dedekind eta function. They have subsequently been much studied in number theory, and have occurred in some problems of topology. Dedekind sums have...

Weierstrass eta function should not be confused with either the Dedekind eta function or the Dirichlet eta function. The Weierstrass p-function is related...

lambda calculus. Mathematics, the Dirichlet eta function, Dedekind eta function, and Weierstrass eta function. In category theory, the unit of an adjunction...

Euler function, which is closely related to the Dedekind eta function. The Jacobi theta function may be written in terms of the Ramanujan theta function as:...

discriminant The Dedekind eta function is defined as η ( z ) = q 1 / 24 ∏ n = 1 ∞ ( 1 − q n ) , q = e 2 π i z . {\displaystyle \eta (z)=q^{1/24}\prod...

24 {\displaystyle \Delta =(2\pi )^{12}\eta ^{24}} where η {\displaystyle \eta } is the Dedekind eta function. For the Fourier coefficients of Δ {\displaystyle...

Richard Dedekind Dedekind cut Dedekind domain Dedekind eta function Dedekind-infinite set Dedekind number Dedekind psi function Dedekind sum Dedekind zeta...

a real analytic Eisenstein series (or Epstein zeta function) in terms of the Dedekind eta function. There are many generalizations of it to more complicated...

axiom Dedekind completeness Dedekind cut Dedekind discriminant theorem Dedekind domain Dedekind eta function Dedekind function Dedekind group Dedekind number...

{\displaystyle (3n^{2}-n)/2} is a pentagonal number. The Euler function is related to the Dedekind eta function as ϕ ( e 2 π i τ ) = e − π i τ / 12 η ( τ ) . {\displaystyle...

Modular Functions". The function η ( τ ) {\displaystyle \eta (\tau )} is the Dedekind eta function and ( e 2 π i τ ) α {\displaystyle (e^{2\pi i\tau })^{\alpha...

functions Theta functions Neville theta functions Modular lambda function Closely related are the modular forms, which include J-invariant Dedekind eta...

(\theta )|<\pi } , where Γ(z) is the gamma function, and related to a special value of the Dedekind eta function. Expanding into series of powers and equating...

of the Dedekind eta function. The Fourier coefficients here are written τ ( n ) {\displaystyle \tau (n)} and called 'Ramanujan's tau function', with the...

z ) {\displaystyle \eta (z)} denote the Dedekind eta function. Then for q = e 2 π i z {\displaystyle q=e^{2\pi iz}} , the function S ~ ( z ) := q − 1 /...

Euler's function, which is closely related to the Dedekind eta function, and occurs in the study of modular forms. The modulus of the Euler function (see...