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Sbornik: Mathematics, 1996, Volume 187, Issue 9, Pages 1319–1348
DOI: https://doi.org/10.1070/SM1996v187n09ABEH000158 (Mi sm158) 		 
This article is cited in 146 scientific papers (total in 146 papers)

Modular functions and transcendence questions

Yu. V. Nesterenko

M. V. Lomonosov Moscow State University
English version PDF (1215 kB) Citations (146)
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DOI: https://doi.org/10.1070/SM1996v187n09ABEH000158
Abstract: We prove results on the transcendence degree of a field generated by numbers connected with the modular function $j(\tau )$. In particular, we show that $\pi$ and $e^\pi$ are algebraically independent and we prove Bertrand's conjecture on algebraic independence over $\mathbb Q$ of the values at algebraic points of a modular function and its derivatives.
Received: 07.03.1996
Russian version:
Matematicheskii Sbornik, 1996, Volume 187, Number 9, Pages 65–96
DOI: https://doi.org/10.4213/sm158
Bibliographic databases:
UDC: 511.36
MSC: Primary 11J89, 11J85; Secondary 11J91, 11F11
Language: English
Original paper language: Russian
Citation: Yu. V. Nesterenko, “Modular functions and transcendence questions”, Mat. Sb., 187:9 (1996), 65–96; Sb. Math., 187:9 (1996), 1319–1348
Citation in format AMSBIB
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\paper Modular functions and transcendence questions
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\transl
\jour Sb. Math.
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    • This publication is cited in the following 146 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:2520
    Russian version PDF:1493
    English version PDF:145
    References:197
    First page:3
     
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