General divisor functions in arithmetic progressions to large moduli

TL;DR

This paper investigates how general divisor functions are distributed in arithmetic progressions with large, smooth moduli that surpass the square root of the function's length, expanding understanding of their behavior in number theory.

Contribution

It establishes new results on the distribution of divisor functions in arithmetic progressions with large smooth moduli exceeding the square root of their length.

Findings

Distribution results for divisor functions in large smooth moduli

Extension beyond square root of length for moduli

Improved understanding of divisor functions in arithmetic progressions

Abstract

We prove a result on the distribution of the general divisor functions in arithmetic progressions to smooth moduli which exceed the square root of the length.