THE MIXED JOINT FUNCTIONAL INDEPENDENCE OF THE RIEMANN ZETA- AND PERIODIC HURWITZ ZETA-FUNCTIONS
https://doi.org/10.22405/2226-8383-2016-17-4-57-64
Abstract
The functional independence of zeta-functions is an interesting nowadays problem. This problem comes back to D. Hilbert. In 1900, at the International Congress of Mathematicians in Paris, he conjectured that the Riemman zeta-function does not satisfy any algebraicdifferential equation. This conjecture was solved by A. Ostrowski. In 1975, S.M. Voronin proved the functional independence of the Riemann zeta-function. After that many mathematicians obtained the functional independence of certain zeta- and L-functions. In the present paper, the joint functional independence of a collection consisting of the Riemann zeta-function and several periodic Hurwitz zeta-functions with parameters algebraically independent over the field of rational numbers is obtained. Such type of functional independence is called as “mixed functional independence” since the Riemann zeta-function has Euler product expansion over primes while the periodic Hurwitz zeta-functions do not have Euler product.
About the Authors
R. Kaˇcinskait˙
Siauliai University
Lithuania
Lithuania
doctor of Physical Sciences (Mathematics), professor, Department of Mathematics, Faculty of Technology, Physical and Biomedical Sciences
S. Rapimbergait˙e
Siauliai University
Lithuania
Lithuania
master of Physical Sciences (Mathematics), Department of Mathematics, Faculty of Technology, Physical and Biomedical Sciences
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Review
For citations:
Kaˇcinskait˙ R., Rapimbergait˙e S. THE MIXED JOINT FUNCTIONAL INDEPENDENCE OF THE RIEMANN ZETA- AND PERIODIC HURWITZ ZETA-FUNCTIONS. Chebyshevskii Sbornik. 2016;17(4):57-64. (In Russ.) https://doi.org/10.22405/2226-8383-2016-17-4-57-64
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