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...

{1}{(q^{2};q^{5})_{\infty }(q^{3};q^{5})_{\infty }}}} The Dedekind eta function identities for the functions G and H result by combining only the following two...

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...

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

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...

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

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

pronounce Dedekind. List of things named after Richard Dedekind Dedekind cut Dedekind domain Dedekind eta function Dedekind-infinite set Dedekind number...

{\displaystyle \phi } is the Euler function, η {\displaystyle \eta } is the Dedekind eta function, and the function Δ ( z ) {\displaystyle \Delta (z)}...

certain product of values of the gamma function at rational values in terms of values of the Dedekind eta function at imaginary quadratic irrational numbers...

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...

specifically the Dedekind eta function. The same sequence of pentagonal numbers appears in a recurrence relation for the partition function: p ( n ) = ∑ k...

{\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...

)^{3}-27g_{3}(\tau )^{2}=(2\pi )^{12}\,\eta ^{24}(\tau )} , Dedekind eta function η ( τ ) {\displaystyle \eta (\tau )} , and modular invariants, g 2 (...

Technical Approvals Dedekind eta function Dirichlet eta function Eta conversion Eta invariant Weierstrass eta function The small letter eta is used as 't Hooft...

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

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

{3}+12256q^{4}+39350q^{5}+\dots \end{aligned}}} and η(τ) is the Dedekind eta function. Norton & Wilson (1986) found the 14 conjugacy classes of maximal...

(\tau )=k^{2}(\tau )} . In terms of the Dedekind eta function η ( τ ) {\displaystyle \eta (\tau )} and theta functions, λ ( τ ) = ( 2 η ( τ 2 ) η 2 ( 2 τ )...

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...

(\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...

Dedekind eta function and the modular discriminant, which connection is deepened by Monstrous moonshine, a development that related modular functions...

throughout this section since the q-expansion of the j-function (as well as the well-known Dedekind eta function) uses q = e 2 π i τ {\displaystyle q=e^{2\pi i\tau...

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...

\end{aligned}}} with the j-function j(τ), Eisenstein series E4, and Dedekind eta function η(τ). The first expansion is the McKay–Thompson...

q^{3}+1956q^{4}+5135q^{5}+\dots \end{aligned}}} and η(τ) is the Dedekind eta function. It can be defined in terms of the generators a and b and relations...

harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space)...

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

an effect size measure for analyses of variance the eta meson viscosity the Dedekind eta function energy conversion efficiency efficiency (physics) the...