Hurwitz - Bernoulli Numbers, Formal Groups and the L - Functions of Elliptic Curves

TL;DR

This paper develops the theory of L-functions of elliptic curves by drawing an analogy with Euler's classical approach to the Riemann zeta-function, utilizing elliptic functions.

Contribution

It introduces a novel framework connecting elliptic functions with the L-functions of elliptic curves, extending classical methods to a new context.

Findings

Establishes a new approach to L-functions using elliptic functions.

Provides insights into the structure of elliptic curve L-functions.

Bridges classical and modern number theory techniques.

Abstract

Classically, Euler developed the theory of the Riemann zeta - function using as his starting point the exponential and partial fraction forms of cot(z) . In this paper we wish to develop the theory of $L$-functions of elliptic curves starting from the theory of elliptic functions in an analogous manner.