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

8 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

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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.",

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AU - McGown, Kevin

AU - Treviño, Enrique

AU - Trudgian, Tim

PY - 2016

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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 - https://www.scopus.com/pages/publications/84982769628

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DO - 10.7169/facm/2016.55.2.5

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EP - 225

JO - Functiones et Approximatio, Commentarii Mathematici

JF - Functiones et Approximatio, Commentarii Mathematici

IS - 2

ER -

Resolving Grosswald's conjecture on GRH

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