Lower bounds of discrete moments of the derivatives of the Riemann zeta-function on the critical line
Journal de Théorie des Nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 285-305.

We establish unconditional lower bounds for certain discrete moments of the Riemann zeta-function and its derivatives on the critical line. We use these discrete moments to give unconditional lower bounds for the continuous moments I k,l (T)= 0 T |ζ (l) (1 2+it)| 2k dt, where l is a non-negative integer and k1 a rational number. In particular, these lower bounds are of the expected order of magnitude for I k,l (T).

Nous établissons des bornes inférieures inconditionnelles pour certains moments discrets de la fonction zêta de Riemann et de ses dérivées dans la bande critique. Nous utilisons ces moments discrets pour donner des bornes inférieures inconditionnelles pour les moments continus I k,l (T)= 0 T |ζ (l) (1 2+it)| 2k dt, où l est un entier positif et k1 un nombre rationnel. En particulier, ces bornes inférieures sont de l’ordre de grandeur attendu pour I k,l (T).

Published online:
DOI: 10.5802/jtnb.836
Thomas Christ 1; Justas Kalpokas 2

1 Department of Mathematics Würzburg University Emil-Fischer-Str. 40, 97074 Würzburg
2 Faculty of Mathematics and Informatics Vilnius University Naugarduko 24, 03225 Vilnius, Lithuania
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Thomas Christ; Justas Kalpokas. Lower bounds of discrete moments of the derivatives of the Riemann zeta-function on the critical line. Journal de Théorie des Nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 285-305. doi : 10.5802/jtnb.836. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.836/

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