In mathematics, Eisenstein–Kronecker numbers are an analogue for imaginary quadratic fields of generalized Bernoulli numbers.
[1][2][3] They are defined in terms of classical Eisenstein–Kronecker series, which were studied by Kenichi Bannai and Shinichi Kobayashi using the Poincaré bundle.
[3][4] Eisenstein–Kronecker numbers are algebraic and satisfy congruences that can be used in the construction of two-variable p-adic L-functions.
[3][5] They are related to critical L-values of Hecke characters.
[1][5] When A is the area of the fundamental domain of
divided by
π
{\displaystyle \Gamma }
is a lattice in
(
γ ∈
γ ¯
+ γ
⟨ γ ,
is the complex conjugate of z.