Zeros of the Riemann zeta-function and its universality
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 $\zeta(s+i\gamma_k)$.
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
Affiliations des auteurs :
Ramūnas Garunkštis 1 ; Antanas Laurinčikas 1 ; Renata Macaitienė 2
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author = {Ram\={u}nas Garunk\v{s}tis and Antanas Laurin\v{c}ikas and Renata Macaitien\.{e}},
title = {Zeros of the {Riemann} zeta-function and its universality},
journal = {Acta Arithmetica},
pages = {127--142},
publisher = {mathdoc},
volume = {181},
number = {2},
year = {2017},
doi = {10.4064/aa8583-5-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8583-5-2017/}
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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
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