SMOOTH-SUPPORTED MULTIPLICATIVE FUNCTIONS in ARITHMETIC PROGRESSIONS beyond the x1/2-BARRIER

Sary Drappeau; Andrew Granville; Xuancheng Shao

doi:10.1112/S0025579317000225

SMOOTH-SUPPORTED MULTIPLICATIVE FUNCTIONS in ARITHMETIC PROGRESSIONS beyond the x^1/2-BARRIER

Sary Drappeau, Andrew Granville, Xuancheng Shao

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We show that smooth-supported multiplicative functions are well distributed in arithmetic progressions a1a₂^-1(mod q) on average over moduli q ≥ x^3/5-ϵwith (q,a1a2)=1.

Original language	English
Pages (from-to)	895-918
Number of pages	24
Journal	Mathematika
Volume	63
Issue number	3
DOIs	https://doi.org/10.1112/S0025579317000225
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017 University College London.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/S0025579317000225

Cite this

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title = "SMOOTH-SUPPORTED MULTIPLICATIVE FUNCTIONS in ARITHMETIC PROGRESSIONS beyond the x1/2-BARRIER",

abstract = "We show that smooth-supported multiplicative functions are well distributed in arithmetic progressions a1a2-1(mod q) on average over moduli q ≥ x3/5-ϵwith (q,a1a2)=1.",

author = "Sary Drappeau and Andrew Granville and Xuancheng Shao",

note = "Publisher Copyright: {\textcopyright} 2017 University College London.",

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doi = "10.1112/S0025579317000225",

language = "English",

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pages = "895--918",

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AU - Drappeau, Sary

AU - Granville, Andrew

AU - Shao, Xuancheng

PY - 2017

Y1 - 2017

N2 - We show that smooth-supported multiplicative functions are well distributed in arithmetic progressions a1a2-1(mod q) on average over moduli q ≥ x3/5-ϵwith (q,a1a2)=1.

AB - We show that smooth-supported multiplicative functions are well distributed in arithmetic progressions a1a2-1(mod q) on average over moduli q ≥ x3/5-ϵwith (q,a1a2)=1.

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U2 - 10.1112/S0025579317000225

DO - 10.1112/S0025579317000225

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VL - 63

SP - 895

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JO - Mathematika

JF - Mathematika

IS - 3

ER -