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Color representation of the Dirichlet eta function. It is generated as a Matplotlib plot using a version of the Domain coloring method. [1]In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0: = = = + +.
In mathematics, the classical Kronecker limit formula describes the constant term at s = 1 of 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 Eisenstein series. It is named for Leopold Kronecker.
The cavity method is an alternative method, often of simpler use than the replica method, for studying disordered mean-field problems. It has been devised to deal with models on locally tree-like graphs. Another alternative method is the supersymmetric method. The use of the supersymmetry method provides a mathematical rigorous alternative to ...
In mathematics, 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 η(w) of a lattice vector; The eta function η(s) used to define the eta invariant
the partial regression coefficient in statistics, also interpreted as an effect size measure for analyses of variance; the eta meson; viscosity [33] the Dedekind eta function [34] energy conversion efficiency [35] efficiency (physics) the Minkowski metric tensor in relativity [36] η-conversion in lambda calculus [37]
Dedekind η-function in the upper half-plane. 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 of complex numbers, where the imaginary part is positive. It also occurs in bosonic string theory.
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Here χ is the quadratic residue symbol modulo D, where −D is the discriminant of an imaginary quadratic field. The sum is taken over 0 < r < D, with the usual convention χ(r) = 0 if r and D have a common factor. The function η is the Dedekind eta function, and h is the class number, and w is the number of roots of unity.