Abstract
The purpose of this note is to point out that the paper On algebraic values of function \( \exp (2\pi i x + \log \log y)\) by Igor Nikolaev published in the Ramanujan Journal 47 (2018), 417–425, is erroneous.
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References
Lang, S.: Introduction to Transcendental Numbers. Addison-Wesley Publishing Co., Reading (1966)
Nikolaev, I.: On algebraic values of function \( \exp (2\pi i x + \log \log y)\). Ramanujan J. 47, 417–425 (2018). https://doi.org/10.1007/s11139-017-9969-3
Schappacher, N.: On the History of Hilbert’s Twelfth Problem: A Comedy of Errors. Sémin. Congr. 3, Soc. Math. France, Paris (1998)
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Waldschmidt, M. On a paper by Nikolaev. Ramanujan J 57, 1517–1518 (2022). https://doi.org/10.1007/s11139-021-00406-x
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DOI: https://doi.org/10.1007/s11139-021-00406-x
Keywords
- Hermite–Lindemann Theorem
- Schanuel’s Conjecture
- Hilbert class field
- Kronecker Jugendtraum
- Hilbert 12th problem