# Slice regular functions of several octonionic variables

## TL;DR

This paper introduces a new slice theory for octonionic functions, extending complex analysis concepts to nonassociative octonions, and establishes foundational formulas and phenomena in this novel setting.

## Contribution

It develops a generalized slice theory for octonionic variables, including a Bochner-Martinelli formula and Hartogs phenomena, expanding analysis into nonassociative algebraic structures.

## Key findings

- Established Bochner-Martinelli formula for octonionic slice functions
- Proved Hartogs phenomena for slice regular functions
- Extended complex analysis concepts to octonionic variables

## Abstract

Octonionic analysis is becoming eminent due to the role of octonions in the theory of G2 manifold. In this article, a new slice theory is introduced as a generalization of the holomorphic theory of several complex variables to the noncommutative or nonassociative realm. The Bochner-Martinelli formula is established for slice functions of several octonionic variables as well as several quaternionic variables. In this setting, we find the Hartogs phenomena for slice regular functions