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Large values of the remainder term of the prime number theorem
Virtualconference
Authors : Pintz, Janos (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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.
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2020 Conference Date : 26/11/2020 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:46:24 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-26_Pintz.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireEvent Organizers : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2256.html
Citation Data
DOI : 10.24350/CIRM.V.19689003Cite this video as: 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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