Generation of symmetric exponential sums

TL;DR

This paper introduces a novel method for generating infinite series of symmetric exponential sum identities with applications across mathematics and dynamic systems, analyzing their properties and connections to known sequences.

Contribution

A new method for generating symmetric exponential sum identities, linking them to Morse-Hedlund sequences and magic squares, expanding theoretical understanding.

Findings

Properties of generated identities are analyzed.

Relations to Morse-Hedlund sequence are established.

Connections to magic squares are demonstrated.

Abstract

In this paper, a new method for generation of infinite series of symmetric identities written for exponential sums in real numbers is proposed. Such systems have numerous applications in theory of numbers, chaos theory, algorithmic complexity, dynamic systems, etc. Properties of generated identities are studied. Relations of the introduced method for generation of symmetric exponential sums to the Morse-Hedlund sequence and to the theory of magic squares are established.