On Artin's conjecture on average and short character sums

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dc.contributor.authorKlurman, Oleksiy
dc.contributor.authorShparlinski, Igor E.
dc.contributor.authorTeräväinen, Joni
dc.contributor.organizationfi=matematiikan ja tilastotieteen laitos|en=Department of Mathematics and Statistics|
dc.contributor.organization-code1.2.246.10.2458963.20.46717060993
dc.converis.publication-id498668440
dc.converis.urlhttps://research.utu.fi/converis/portal/Publication/498668440
dc.date.accessioned2025-08-27T21:34:56Z
dc.date.available2025-08-27T21:34:56Z
dc.description.abstract<p>Let N<sub>a</sub>(x) denote the number of primes up to <i>x</i> for which the integer <i>a</i> is a primitive root. We show that N<sub>a</sub>(x) satisfies the asymptotic predicted by Artin's conjecture for almost all 1 ⩽ a ⩽ exp((log log x)<sup>2</sup>). This improves on a result of Stephens (1969). A key ingredient in the proof is a new short character sum estimate over the integers, improving on the range of a result of Garaev (2006).<br></p>
dc.identifier.eissn1469-2120
dc.identifier.jour-issn0024-6093
dc.identifier.olddbid200663
dc.identifier.oldhandle10024/183690
dc.identifier.urihttps://www.utupub.fi/handle/11111/46673
dc.identifier.urlhttps://doi.org/10.1112/blms.70103
dc.identifier.urnURN:NBN:fi-fe2025082789193
dc.language.isoen
dc.okm.affiliatedauthorTeräväinen, Joni
dc.okm.discipline111 Mathematicsen_GB
dc.okm.discipline111 Matematiikkafi_FI
dc.okm.internationalcopublicationinternational co-publication
dc.okm.internationalityInternational publication
dc.okm.typeA1 ScientificArticle
dc.publisherWILEY
dc.publisher.countryUnited Kingdomen_GB
dc.publisher.countryBritanniafi_FI
dc.publisher.country-codeGB
dc.publisher.placeHOBOKEN
dc.relation.doi10.1112/blms.70103
dc.relation.ispartofjournalBulletin of the London Mathematical Society
dc.source.identifierhttps://www.utupub.fi/handle/10024/183690
dc.titleOn Artin's conjecture on average and short character sums
dc.year.issued2025

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