Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2021, Number 6, Pages 3–7 (Mi vmumm4432)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Lindemann–Weierstrass theorem

Yu. V. Nesterenko

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: We discuss issues of algebraic independence for values of the function $e^z$ at algebraic points. The most general result of this kind was established at the end of the 19th century and is called the Lindemann–Weierstrass theorem. This is historically the first theorem on the algebraic independence of numbers and it can be proved now in various ways. Below we propose one more way to prove it.
Key words: algebraic independence, criterion of linear independence, saddle point method, exponential function.
Received: 11.09.2020
English version:
Moscow University Mathematics Bulletin, 2021, Volume 76, Issue 6, Pages 239–243
DOI: https://doi.org/10.3103/S0027132221060073
Bibliographic databases:
Document Type: Article
UDC: 511.4
Language: Russian
Citation: Yu. V. Nesterenko, “Lindemann–Weierstrass theorem”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 6, 3–7; Moscow University Mathematics Bulletin, 76:6 (2021), 239–243
Citation in format AMSBIB
\Bibitem{Nes21}
\by Yu.~V.~Nesterenko
\paper Lindemann--Weierstrass theorem
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2021
\issue 6
\pages 3--7
\mathnet{http://mi.mathnet.ru/vmumm4432}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4400788}
\zmath{https://zbmath.org/?q=an:1490.11072}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2021
\vol 76
\issue 6
\pages 239--243
\crossref{https://doi.org/10.3103/S0027132221060073}
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