On Grosswald's conjecture on primitive roots

Stephen D. Cohen; Tomás Oliveira E Silva; Tim Trudgian

doi:10.4064/aa8109-12-2015

On Grosswald's conjecture on primitive roots

Stephen D. Cohen, Tomás Oliveira E Silva, Tim Trudgian

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

7 Citations (Scopus)

Abstract

Grosswalds conjecture is that g(p), the least primitive root modulo p, satisfies g(p)â‰¤pâˆšâˆ’2 for all p>409. We make progress towards this conjecture by proving that g(p)â‰¤pâˆšâˆ’2 for all 409<p<2.5Ã—1015 and for all p>3.38Ã—1071.

Original language	English
Pages (from-to)	263-270
Number of pages	8
Journal	Acta Arithmetica
Volume	172
Issue number	3
DOIs	https://doi.org/10.4064/aa8109-12-2015
Publication status	Published - 2016

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title = "On Grosswald's conjecture on primitive roots",

abstract = "Grosswalds conjecture is that g(p), the least primitive root modulo p, satisfies g(p){\^a}‰¤p{\^a}ˆ{\v s}{\^a}ˆ{\textquoteright}2 for all p>409. We make progress towards this conjecture by proving that g(p){\^a}‰¤p{\^a}ˆ{\v s}{\^a}ˆ{\textquoteright}2 for all 4093.38{\~A}—1071.",

keywords = "Burgess' bound, Character sums, Prime sieves, Primitive roots",

author = "Cohen, {Stephen D.} and {Oliveira E Silva}, Tom{\'a}s and Tim Trudgian",

year = "2016",

doi = "10.4064/aa8109-12-2015",

language = "English",

volume = "172",

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T1 - On Grosswald's conjecture on primitive roots

AU - Cohen, Stephen D.

AU - Oliveira E Silva, Tomás

AU - Trudgian, Tim

PY - 2016

Y1 - 2016

N2 - Grosswalds conjecture is that g(p), the least primitive root modulo p, satisfies g(p)â‰¤pâˆšâˆ’2 for all p>409. We make progress towards this conjecture by proving that g(p)â‰¤pâˆšâˆ’2 for all 4093.38Ã—1071.

AB - Grosswalds conjecture is that g(p), the least primitive root modulo p, satisfies g(p)â‰¤pâˆšâˆ’2 for all p>409. We make progress towards this conjecture by proving that g(p)â‰¤pâˆšâˆ’2 for all 4093.38Ã—1071.

KW - Burgess' bound

KW - Character sums

KW - Prime sieves

KW - Primitive roots

UR - http://www.scopus.com/inward/record.url?scp=84958740980&partnerID=8YFLogxK

U2 - 10.4064/aa8109-12-2015

DO - 10.4064/aa8109-12-2015

M3 - Article

SN - 0065-1036

VL - 172

SP - 263

EP - 270

JO - Acta Arithmetica

JF - Acta Arithmetica

IS - 3

ER -

On Grosswald's conjecture on primitive roots

Abstract

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