Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Collection Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Organizer(s) Rivat, Joël ; Tichy, Robert

Date(s) 23/11/2020 - 27/11/2020

linked URL https://www.chairejeanmorlet.com/2256.html

00:00:00 / 00:00:00

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Large values of the remainder term of the prime number theorem

By János Pintz

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.

Information about the video

Date of recording 26/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19689003
Cite this video Pintz, János (26/11/2020). Large values of the remainder term of the prime number theorem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19689003
URL https://dx.doi.org/10.24350/CIRM.V.19689003

Domain(s)

Number Theory

MSC codes

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