| Title |
Universality in short intervals of the Riemann zeta-function twisted by non-trivial zeros / |
| Authors |
Laurinčikas, Antanas ; Šiaučiūnas, Darius |
| DOI |
10.3390/math8111936 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2020, vol. 8, iss. 11, art. no. 1936, p. [1-14].. ISSN 2227-7390. eISSN 2227-7390 |
| Keywords [eng] |
Montgomery pair correlation conjecture ; non-trivial zeros ; Riemann zeta-function ; universality |
| Abstract [eng] |
Let 0 < γ 1 < γ 2 < ··· 6 γ k 6 ··· 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 { γ k } in the intervals [ N , N + M ] with N 1/2 + ε 6 M 6 N , we prove that the set of shifts ζ ( s + ihγ k ) , h > 0, approximating any non-vanishing analytic function defined in the strip { s ∈ C : 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 )). |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2020 |
| CC license |
|
