English
Large values of the remainder term of the prime number theorem
Virtualconference
Auteurs : Pintz, Janos (Auteur de la Conférence)
CIRM (Editeur )
11M26 - Nonreal zeros of $ \zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
11N05 - Distribution of primes
11N30 - Turan theory, See also {30Bxx}
CIRM (Editeur )
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Résumé :
In the lecture we prove a lower estimate for the average of the absolute value of the remainder term of the prime number theorem which depends in an explicit way on a given zero of the Riemann Zeta Function. The estimate is only interesting if this hypothetical zero lies off the critical line which naturally implies the falsity of the Riemann Hypothesis. (If the Riemann Hypothesis is true, stronger results areobtainable by other metods.) The first explicit results in this direction were proved by Turán and Knapowski in the 1950s, answering a problem of Littlewood from the year 1937. They used the power sum method of Turán. Our present approach does not use Turán's method and gives sharper results.
Codes MSC : 11M26 - Nonreal zeros of $ \zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
11N05 - Distribution of primes
11N30 - Turan theory, See also {30Bxx}
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/12/2020 Date de captation : 26/11/2020 Sous collection : Research talks arXiv category : Number Theory Domaine : Number Theory Format : MP4 (.mp4) - HD Durée : 00:46:24 Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-26_Pintz.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19689003Citer cette vidéo: Pintz, Janos (2020). Large values of the remainder term of the prime number theorem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19689003 URI : http://dx.doi.org/10.24350/CIRM.V.19689003 |
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