Algebraic Structures of Bernoulli Numbers and Polynomials

TL;DR

This paper explores algebraic structures within Laurent series to derive identities involving Bernoulli numbers and polynomials, revealing new relationships through the construction of a specialized subring and module over a Weyl algebra.

Contribution

It introduces a novel algebraic framework in Laurent series for deriving identities of Bernoulli numbers and polynomials, connecting them to Weyl algebra modules.

Findings

Derived new identities of Bernoulli numbers and polynomials

Constructed a subring with a module structure over a Weyl algebra

Established algebraic relationships in Laurent series context

Abstract

In a field of Laurent series, we construct a subring which has a module structure over a Weyl algebra. Identities of Bernoulli numbers and polynomials are obtained from these algebraic structures.