On a weighted sum over multiplicative functions and its applications to the GPY sieve

TL;DR

This paper studies the asymptotic behavior of weighted sums over multiplicative functions and enhances the GPY sieve method with more computationally accessible coefficient expressions.

Contribution

It provides new asymptotic formulas for weighted sums over multiplicative functions and improves the GPY sieve's coefficients for better numerical implementation.

Findings

Derived stronger asymptotic formulas for weighted sums

Enhanced the GPY sieve with computationally friendly coefficients

Facilitated numerical applications of the sieve method

Abstract

In this paper, we investigate the asymptotics of a class of weighted sums over multiplicative functions and apply our results to deduce a stronger asymptotic form of Yitang Zhang's smoothened GPY sieve with coefficient expressions that are friendly to numerical computations.