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math.NT2026
The generalized Montgomery-Hooley formula: A survey
Robert C. Vaughan
This memoir is a survey of theorems and inequalities which have grown out of, and extended, the seminal estimate of Montgomery \cite{HM70} \begin{multline*} V(x,Q)=\sum_{q\le Q}\su…
math.NT2023
Squarefree density of polynomials
J. M. Kowalski, R. C Vaughan
This paper is concerned with squarefree values of polynomials and their density in large boxes centered at the origin.
math.NT2020
On generating functions in additive number theory, II: Lower-order terms and applications to PDEs
Julia Brandes, Scott T. Parsell, Konstantinos Poulias +2
We obtain asymptotics for sums of the form involving lower order main terms. As an application, we show that for almost all one…