# A family of multiple integrals connected with relatives of the Dickman function

## TL;DR

This paper develops an asymptotic expansion for a family of multiple integrals related to the Dickman function and explores their arithmetic structure, extending previous work on the Dickman function.

## Contribution

Introduces an asymptotic expansion for integrals linked to Dickman relatives, revealing their arithmetic structure and extending prior research.

## Key findings

- Derived an asymptotic expansion for the integrals
- Identified the arithmetic structure of the coefficients
- Connected the results to previous work on the Dickman function

## Abstract

We present an asymptotic expansion for a family of multiple integrals connected with relatives of the Dickman function. The coefficients of this expansion have a similar arithmetic structure as those appearing in work of Soundararajan on an analogous expansion for the Dickman function.