A simple and self-contained proof for the Lindemann-Weierstrass theorem. (English) Zbl 07918585
Guàrdia, Jordi (ed.) et al., New frontiers in number theory and applications. Cham: Birkhäuser. Trends Math., 349-366 (2024).
For the entire collection see [Zbl 1539.11005].
MSC:
| 11J81 | Transcendence (general theory) |
References:
| [1] | A. Baker, Transcendental Number Theory (Cambridge University Press, New York, 1975) · Zbl 0297.10013 |
| [2] | E. Delaygue, A Lindemann-Weierstrass theorem for E-functions. arXiv:2210.12046v1 [math.NT], 21 Oct 2022 |
| [3] | D.S. Dummit, R.M. Foote, Abstract Algebra, 2nd edn. (John Wiley & Sons, Inc. New York, 2003) |
| [4] | C. Hermite, Sur la fonction exponentielle, vol. 77 (C. R. Acad. Sci., Paris, 1873), pp. 18-24 · JFM 05.0248.01 |
| [5] | D. Hilbert, Über die Transcendenz der Zahlen \(e\) und \(\pi \). Math. Ann. 43, 216-219 (1893) · JFM 25.0734.01 |
| [6] | A. Hurwitz, Beweis der Transcendenz der Zahl \(e\). Math. Ann. 43, 220-222 (1893) |
| [7] | S. Lang, Algebra, revised 3rd edn. (Springer, New York, 2002) · Zbl 0984.00001 |
| [8] | F. Lindemann, Über die Zahl \(\pi \). Math. Ann. 20, 213-225 (1882) · JFM 14.0369.04 |
| [9] | F. Lindemann, Über die Ludolph’sche Zahl. Sitzungsberichte der Königlich Preussischen Akademie der Wissenchaften zu Berlin 2, 679-682 (1882) · JFM 14.0369.02 |
| [10] | S.A. Popescu, Hermite Principle, Lindemann’s idea and simple proofs for the basic results in the irrationality and transcendence of some numbers. A tribute to the 80th birthday of Prof. Gavriil Păltineanu. Rom. J. Math. Comput. Sci. 12(2), 28-51 (2022) · Zbl 07806219 |
| [11] | K. Weierstrass, Zu Lindemann Abhandlung “Über die Ludolph’sche Zahl, ” Sitzungsberichte der Königlich Preussischen Akademie der Wissenchaften zu Berlin 5, 1067-1085 (1885) |
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