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Universality in Short Intervals of the Riemann Zeta-Function Twisted by Non-Trivial Zeros

1
Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
2
Regional Development Institute, Šiauliai University, P. Višinskio str. 25, LT-76351 Šiauliai, Lithuania
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(11), 1936; https://doi.org/10.3390/math8111936
Received: 3 October 2020 / Revised: 18 October 2020 / Accepted: 20 October 2020 / Published: 3 November 2020
Let 0<γ1<γ2<γk be the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function ζ(s). Using a certain estimate on the pair correlation of the sequence {γk} in the intervals [N,N+M] with N1/2+εMN, we prove that the set of shifts ζ(s+ihγk), h>0, approximating any non-vanishing analytic function defined in the strip {sC:1/2<Res<1} with accuracy ε>0 has a positive lower density in [N,N+M] as N. Moreover, this set has a positive density for all but at most countably ε>0. The above approximation property remains valid for certain compositions F(ζ(s)). View Full-Text
Keywords: Montgomery pair correlation conjecture; non-trivial zeros; Riemann zeta-function; universality Montgomery pair correlation conjecture; non-trivial zeros; Riemann zeta-function; universality
MDPI and ACS Style

Laurinčikas, A.; Šiaučiūnas, D. Universality in Short Intervals of the Riemann Zeta-Function Twisted by Non-Trivial Zeros. Mathematics 2020, 8, 1936. https://doi.org/10.3390/math8111936

AMA Style

Laurinčikas A, Šiaučiūnas D. Universality in Short Intervals of the Riemann Zeta-Function Twisted by Non-Trivial Zeros. Mathematics. 2020; 8(11):1936. https://doi.org/10.3390/math8111936

Chicago/Turabian Style

Laurinčikas, Antanas, and Darius Šiaučiūnas. 2020. "Universality in Short Intervals of the Riemann Zeta-Function Twisted by Non-Trivial Zeros" Mathematics 8, no. 11: 1936. https://doi.org/10.3390/math8111936

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