Greedy Sums and Dirichlet Series

TL;DR

This paper proves that the greedy sum of a product of two complex arrays equals the product of their individual greedy sums, under the condition that all sums exist, extending understanding of sum operations in complex analysis.

Contribution

It establishes a new property relating greedy sums and products of complex arrays, providing conditions for their equivalence.

Findings

Greedy sum of a product equals product of sums when all sums exist.

Provides a theoretical foundation for sum operations in complex arrays.

Extends previous results in sum theory to complex number arrays.

Abstract

We prove that the greedy sum of a direct product of two numeric arrays of complex numbers is equal to the product of the greedy sums of the factors provided that all the mentioned sums exist.