mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, Eisenstein–Kronecker numbers are an analogue for

imaginary quadratic field In algebraic number theory, a quadratic field is an algebraic number field of degree two over \mathbf, the rational numbers. Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free integer different from 0 an ...

s of generalized Bernoulli numbers. They are defined in terms of classical Eisenstein–Kronecker series, which were studied by Kenichi Bannai and Shinichi Kobayashi using the

Poincaré bundle In mathematics, a dual abelian variety can be defined from an abelian variety ''A'', defined over a field ''K''. Definition To an abelian variety ''A'' over a field ''k'', one associates a dual abelian variety ''A''v (over the same field), which is ...

. Eisenstein–Kronecker numbers are algebraic and satisfy congruences that can be used in the construction of two-variable ''p''-adic ''L''-functions. They are related to critical ''L''-values of

Hecke character In number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of ''L''-functions larger than Dirichlet ''L''-functions, and a natural setting for the Dedekind zeta-functions and ce ...

References

{{DEFAULTSORT:Eisenstein-Kronecker number Number theory