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Algebraic independence of exponents

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Three theorems are obtained for the algebraic independence of some numbers related to exponential functions. Theorems 1 and 3 are extensions of the well-known Gelfond results.

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Literature cited

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Translated from Matematicheskie Zametki, Vol. 17, No. 3, pp. 407–418, March, 1975.

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Shmelev, A.A. Algebraic independence of exponents. Mathematical Notes of the Academy of Sciences of the USSR 17, 236–243 (1975). https://doi.org/10.1007/BF01149013

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  • Exponential Function
  • Algebraic Independence