# An elliptic analogue of Fukuhara's trigonometeric identities

## TL;DR

This paper introduces new elliptic function identities that extend Fukuhara's trigonometric identities, revealing reciprocity laws for elliptic Dedekind sums through Laurent expansion coefficients.

## Contribution

It presents novel elliptic identities as an analogue to known trigonometric identities and links them to reciprocity laws for elliptic Dedekind sums.

## Key findings

- New elliptic identities derived as analogues of Fukuhara's trigonometric identities
- Laurent expansion coefficients lead to reciprocity laws for elliptic Dedekind sums
- Establishes connections between elliptic functions and number theory

## Abstract

We obtain new elliptic function identities, which are an elliptic analogue of Fukuhara's trigonometric identities. We show that the coefficients of Laurent expansions at $z=0$ of our elliptic identities give rise to some reciprocity laws for elliptic Dedekind sums.