Geodesic
Zeros of the Riemann zeta-function and its universality
Ramūnas Garunkštis1 ; Antanas Laurinčikas1 ; Renata Macaitienė2
1 Faculty of Mathematics and Informatics Vilnius University Naugarduko St. 24 LT-03225 Vilnius, Lithuania
2 Research Institute Šiauliai University P. Višinskio St. 25 LT-76351 Šiauliai, Lithuania
Acta Arithmetica, Tome 181 (2017) no. 2, pp. 127-142.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $0 \lt \gamma_1\leq \gamma_2 \leq\cdots$ be the imaginary parts of non-trivial zeros of the Riemann zeta-function $\zeta(s)$. Using the Montgomery conjecture (its weaker form) on the pair correlation of the sequence $\{\gamma_k\}$, we show that analytic functions of a wide class can be approximated by shifts $\zeta(s+i\gamma_k)$.
DOI : 10.4064/aa8583-5-2017
Keywords: gamma leq gamma leq cdots imaginary parts non trivial zeros riemann zeta function zeta using montgomery conjecture its weaker form pair correlation sequence gamma analytic functions wide class approximated shifts zeta gamma

Ramūnas Garunkštis 1 ; Antanas Laurinčikas 1 ; Renata Macaitienė 2

1 Faculty of Mathematics and Informatics Vilnius University Naugarduko St. 24 LT-03225 Vilnius, Lithuania
2 Research Institute Šiauliai University P. Višinskio St. 25 LT-76351 Šiauliai, Lithuania 
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Ramūnas Garunkštis; Antanas Laurinčikas; Renata Macaitienė. Zeros of the Riemann zeta-function and its universality. Acta Arithmetica, Tome 181 (2017) no. 2, pp. 127-142. doi : 10.4064/aa8583-5-2017. http://geodesic.mathdoc.fr/articles/10.4064/aa8583-5-2017/

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