Resolving Grosswald's conjecture on GRH

Kevin McGown; Enrique Treviño; Tim Trudgian

doi:10.7169/facm/2016.55.2.5

Resolving Grosswald's conjecture on GRH

Kevin McGown, Enrique Treviño, Tim Trudgian

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

7 Citations (Scopus)

Abstract

In this paper we examine Grosswald's conjecture on g(p), the least primitive root modulo p. Assuming the Generalized Riemann Hypothesis (GRH), and building on previous work by Cohen, Oliveira e Silva and Trudgian, we resolve Grosswald's conjecture by showing that g(p) < √p - 2 for all p > 409. Our method also shows that under GRH we have â(p) > √ p - 2 for all p > 2791, where ĝ(p) is the least prime primitive root modulo p.

Original language	English
Pages (from-to)	215-225
Number of pages	11
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	55
Issue number	2
DOIs	https://doi.org/10.7169/facm/2016.55.2.5
Publication status	Published - 2016

Access to Document

10.7169/facm/2016.55.2.5

Cite this

@article{bc0406e0a4a54b87a1d1b4f254914f5d,

title = "Resolving Grosswald's conjecture on GRH",

abstract = "In this paper we examine Grosswald's conjecture on g(p), the least primitive root modulo p. Assuming the Generalized Riemann Hypothesis (GRH), and building on previous work by Cohen, Oliveira e Silva and Trudgian, we resolve Grosswald's conjecture by showing that g(p) < √p - 2 for all p > 409. Our method also shows that under GRH we have {\^a}(p) > √ p - 2 for all p > 2791, where ĝ(p) is the least prime primitive root modulo p.",

keywords = "Character sums, Generalised Riemann hypothesis, Prime sieves, Primitive roots",

author = "Kevin McGown and Enrique Trevi{\~n}o and Tim Trudgian",

year = "2016",

doi = "10.7169/facm/2016.55.2.5",

language = "English",

volume = "55",

pages = "215--225",

journal = "Functiones et Approximatio, Commentarii Mathematici",

issn = "0208-6573",

publisher = "Adam Mickiewicz University Press",

number = "2",

}

TY - JOUR

T1 - Resolving Grosswald's conjecture on GRH

AU - McGown, Kevin

AU - Treviño, Enrique

AU - Trudgian, Tim

PY - 2016

Y1 - 2016

N2 - In this paper we examine Grosswald's conjecture on g(p), the least primitive root modulo p. Assuming the Generalized Riemann Hypothesis (GRH), and building on previous work by Cohen, Oliveira e Silva and Trudgian, we resolve Grosswald's conjecture by showing that g(p) < √p - 2 for all p > 409. Our method also shows that under GRH we have â(p) > √ p - 2 for all p > 2791, where ĝ(p) is the least prime primitive root modulo p.

AB - In this paper we examine Grosswald's conjecture on g(p), the least primitive root modulo p. Assuming the Generalized Riemann Hypothesis (GRH), and building on previous work by Cohen, Oliveira e Silva and Trudgian, we resolve Grosswald's conjecture by showing that g(p) < √p - 2 for all p > 409. Our method also shows that under GRH we have â(p) > √ p - 2 for all p > 2791, where ĝ(p) is the least prime primitive root modulo p.

KW - Character sums

KW - Generalised Riemann hypothesis

KW - Prime sieves

KW - Primitive roots

UR - http://www.scopus.com/inward/record.url?scp=84982769628&partnerID=8YFLogxK

U2 - 10.7169/facm/2016.55.2.5

DO - 10.7169/facm/2016.55.2.5

M3 - Article

SN - 0208-6573

VL - 55

SP - 215

EP - 225

JO - Functiones et Approximatio, Commentarii Mathematici

JF - Functiones et Approximatio, Commentarii Mathematici

IS - 2

ER -

Resolving Grosswald's conjecture on GRH

Abstract

Access to Document

Other files and links

Fingerprint

Cite this