On the Nature of gamma-th Arithmetic Zeta Functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50016902" target="_blank" >RIV/62690094:18470/20:50016902 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2073-8994/12/5/790" target="_blank" >https://www.mdpi.com/2073-8994/12/5/790</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym12050790" target="_blank" >10.3390/sym12050790</a>

Result language
angličtina
Original language name
On the Nature of gamma-th Arithmetic Zeta Functions
Original language description
Symmetry and elementary symmetric functions are main components of the proof of the celebrated Hermite-Lindemann theorem (about the transcendence of e^alpha, for algebraic values of alpha) which settled the ancient Greek problem of squaring the circle. In this paper, we are interested in similar results, but for powers such as e^{gamma log n}. This kind of problem can be posed in the context of arithmetic functions. More precisely, we study the arithmetic nature of the so-called gamma -th arithmetic zeta function, for a positive integer n and a complex number gamma. Moreover, we raise a conjecture about the exceptional set of zeta_gamma, in the case in which gamma is transcendental, and we connect it to the famous Schanuel's conjecture.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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