Schanuel's conjecture
conjecture concerning the transcendence degree of field extensions of the rational numbers
Facts
7 properties- Instance of
- conjecture
- Defining formula
- \forall z_1,\dots,z_n\in\mathbb C\colon\dim(\mathbb Qz_1+\cdots+\mathbb Qz_n)=n\implies\operatorname{trdeg}_{\mathbb Q}\mathbb Q(z_1,\dots,z_n,\exp z_1,\dots,\exp z_n)\ge n[3]
- Generalization of
- Lindemann–Weierstrass theorem, Baker's theorem, Gelfond–Schneider theorem, Four exponentials conjecture[11][12][13][14]
- Maintained by WikiProject
- WikiProject Mathematics[5]
- Named after
- Stephen Schanuel[2]
- Studied by
- transcendental number theory[4]
🏷️ Also known as
en Schanuel's conjecture
de Schanuelvermutung
de Vermutung von Schanuel
es Conjetura de Schanuel
fi Schanuelin konjektuuri
fr conjecture de Schanuel
it Congettura di Schanuel
ja シャニュエル予想
ja シャヌエル予想
ko 섀뉴얼 추측
pt conjectura de Schanuel
ro conjectura lui Schanuel
zh Schanuel猜想
zh 沙努爾猜想
🔖 Identifiers · 5
- Freebase ID
- /m/06gf5k
- MathWorld ID
- SchanuelsConjecture
- Microsoft Academic ID (discontinued)
- 2779951699
- NLab ID
- Schanuel's conjecture
- ProofWiki ID
- Schanuel's_Conjecture
🔗 Connections
Generalization of 3
Instance of 1
Maintained by WikiProject 1
Named after 1
Studied by 1
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Summary
Schanuel's conjecture is a conjecture[1].