A Primer on Zeta Functions and Decomposition Spaces

TL;DR

This paper introduces the concept of decomposition spaces from homotopy theory to number theorists, aiming to establish a foundation for applying these ideas to the study of zeta functions.

Contribution

It bridges homotopy theory and number theory by explaining decomposition spaces and proposing their potential use in analyzing zeta functions.

Findings

Introduces decomposition spaces to number theorists.

Lays foundational concepts for future research.

Suggests applications of homotopy theory in zeta function analysis.

Abstract

Many examples of zeta functions in number theory and combinatorics are special cases of a construction in homotopy theory known as a decomposition space. This article aims to introduce number theorists to the relevant concepts in homotopy theory and lays some foundations for future applications of decomposition spaces in the theory of zeta functions.