Schanuel's Conjecture and the Transcendence of Power Towers
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018065" target="_blank" >RIV/62690094:18470/21:50018065 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/9/7/717" target="_blank" >https://www.mdpi.com/2227-7390/9/7/717</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math9070717" target="_blank" >10.3390/math9070717</a>
Alternative languages
Result language
angličtina
Original language name
Schanuel's Conjecture and the Transcendence of Power Towers
Original language description
We give three consequences of Schanuel's Conjecture. The first is that P(e)(Q(e)) and P(pi)(Q(pi)) are transcendental, for any non-constant polynomials P(x),Q(x) is an element of Q vertical bar x vertical bar. The second is that pi not equal alpha(beta), for any algebraic numbers alpha and beta. The third is the case of the Gelfond's conjecture (about the transcendence of a finite algebraic power tower) in which all elements are equal.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics
ISSN
2227-7390
e-ISSN
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Volume of the periodical
9
Issue of the periodical within the volume
7
Country of publishing house
CH - SWITZERLAND
Number of pages
6
Pages from-to
"Article Number: 717"
UT code for WoS article
000638687000001
EID of the result in the Scopus database
2-s2.0-85103326176