Abstract
By the Ostrowski theorem, the Riemann zeta-function \(\zeta (s)\) does not satisfy any algebraic-differential equation. Voronin proved that the function \(\zeta (s)\) does not satisfy algebraic-differential equation with continuous coefficients. In the paper, a joint generalization of the Voronin theorem is given, i. e., that a collection \((\zeta (s_1), \dots , \zeta (s_r))\) does not satisfy a certain algebraic-differential equation with continuous coefficients.
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Communicated by B. Sury.
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Korolev, M., Laurinčikas, A. Joint Functional Independence of the Riemann Zeta-Function. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00585-5
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DOI: https://doi.org/10.1007/s13226-024-00585-5
Keywords
- Algebraic-differential independence
- Functional independence
- Gram function
- Riemann zeta-function
- Universality