设 
和 
是两组在有理数域上线性无关的复数。则以下至少有一个是
 |
是 超越数 (Waldschmidt 1979, p. 3.5)。这个定理归功于 Siegel、Schneider、Lang 和 Ramachandra。将 
替换为 
得到的相应陈述被称为四指数猜想，并且尚未被证明。
六指数定理
另请参阅
四指数猜想, Hermite-Lindemann 定理, 超越数使用 Wolfram|Alpha 探索
参考文献
Finch, S. R. "Powers of 3/2 Modulo One." §2.30.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 194-199, 2003.Ramachandra, K. "Contributions to the Theory of Transcendental Numbers. I, II." Acta Arith. 14, 65-78, 1967-68.Ramachandra, K. and Srinivasan, S. "A Note to a Paper: 'Contributions to the Theory of Transcendental Numbers. I, II' by Ramachandra on Transcendental Numbers." Hardy-Ramanujan J. 6, 37-44, 1983.Waldschmidt, M. Transcendence Methods. Queen's Papers in Pure and Applied Mathematics, No. 52. Kingston, Ontario, Canada: Queen's University, 1979.Waldschmidt, M. "On the Transcendence Method of Gel'fond and Schneider in Several Variables." In New Advances in Transcendence Theory (Ed. A. Baker). Cambridge, England: Cambridge University Press, pp. 375-398, 1988.在 Wolfram|Alpha 中被引用
六指数定理请引用为
Weisstein, Eric W. "六指数定理。" 来自 MathWorld——Wolfram Web 资源。 https://mathworld.net.cn/SixExponentialsTheorem.html