# On Euler-Ramanujan formula, Dirichlet series and minimal surfaces

## TL;DR

This paper explores connections between Euler-Ramanujan identities, Dirichlet series, and minimal surfaces, deriving functional equations and identities through complex analysis and geometric representations.

## Contribution

It introduces new identities linking Dirichlet series with minimal surface representations and derives their functional equations, expanding the understanding of these mathematical structures.

## Key findings

- Derived functional equations for Dirichlet series related to Euler-Ramanujan identities
- Established identities involving Dirichlet series and minimal surfaces
- Reformulated Euler-Ramanujan identities in terms of Dirichlet series

## Abstract

In this paper, we rewrite two forms of an Euler-Ramanujan identity in terms of certain Dirichlet series and derive functional equation of the latter. We also use the Weierstrass-Enneper representation of minimal surfaces to obtain some identities involving these Dirichlet series and one complex parameter.