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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&apos;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&apos;s conjecture (about the transcendence of a finite algebraic power tower) in which all elements are equal.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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