Extension of the functional independence of the Riemann zeta-function
In 1972, Voronin proved the functional independence of the Riemann zeta-function ζ(s), i. e., if the functions φj are continuous in ℂN and φ0(ζ(s), …, ζ(N-1)(s))+ ∙∙∙ + sn φn(ζ(s), …, ζ(N-1)(s)) ≡ 0, then φj≡ 0 for j=0,…, n. The problem goes back to Hilbert who obtained the algebraic-differential in...
| Permalink: | http://skupnikatalog.nsk.hr/Record/nsk.NSK01001098346/Details |
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| Matična publikacija: |
Glasnik matematički (Online) 55 (2020), 1 ; str. 55-65 |
| Glavni autor: | Laurinčikas, Antanas (Author) |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.3336/gm.55.1.05 Hrčak |
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| 024 | 7 | |2 doi |a 10.3336/gm.55.1.05 | |
| 035 | |a (HR-ZaNSK)001098346 | ||
| 040 | |a HR-ZaNSK |b hrv |c HR-ZaNSK |e ppiak | ||
| 041 | 0 | |a eng |b eng | |
| 042 | |a croatica | ||
| 044 | |a ci |c hr | ||
| 080 | 1 | |a 51 |2 2011 | |
| 100 | 1 | |a Laurinčikas, Antanas |4 aut | |
| 245 | 1 | 0 | |a Extension of the functional independence of the Riemann zeta-function |h [Elektronička građa] / |c Antanas Laurinčikas. |
| 504 | |a Bibliografske bilješke na kraju teksta. | ||
| 504 | |a Abstract. | ||
| 520 | |a In 1972, Voronin proved the functional independence of the Riemann zeta-function ζ(s), i. e., if the functions φj are continuous in ℂN and φ0(ζ(s), …, ζ(N-1)(s))+ ∙∙∙ + sn φn(ζ(s), …, ζ(N-1)(s)) ≡ 0, then φj≡ 0 for j=0,…, n. The problem goes back to Hilbert who obtained the algebraic-differential independence of ζ(s). In the paper, the functional independence of compositions F(ζ(s)) for some classes of operators F in the space of analytic functions is proved. For example, as a particular case, the functional independence of the function cosζ(s) follows. | ||
| 653 | 0 | |a Algebra |a Analitičke funkcije |a Riemannova zeta-funkcija |a Diferencijalna neovisnost | |
| 773 | 0 | |t Glasnik matematički (Online) |x 1846-7989 |g 55 (2020), 1 ; str. 55-65 |w nsk.(HR-ZaNSK)000659858 | |
| 981 | |b Be2020 |b B03/20 | ||
| 998 | |b tino2106 | ||
| 856 | 4 | 0 | |u https://doi.org/10.3336/gm.55.1.05 |
| 856 | 4 | 0 | |u https://hrcak.srce.hr/239046 |y Hrčak |
| 856 | 4 | 1 | |y Digitalna.nsk.hr |