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The Riemann Hypothesis-Millennium Prize Problem
Karaganda State University, Karagandy, Kazakhstan
- 1 Karaganda State University, Karagandy, Kazakhstan
Advances in Pure Mathematics·Volume 06 (2016)·Pages 915–920·Published 8 November 2016·DOI10.4236/apm.2016.612069
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Abstract
This work is dedicated to the promotion of the results C. Muntz obtained modifying zeta functions. The properties of zeta functions are studied; these properties lead to new regularities of zeta functions. The choice of a special type of modified zeta functions allows estimating the Riemann’s zeta function and solving Riemann Problem-Millennium Prize Problem.
KeywordsEulerChebyshevDirichletRiemannHypothesisZeta FunctionMuntzFunctionComplex NumbersRegular FunctionIntegral Function RepresentationMillennium Prize Problem
- Euler, L. (1988) Introduction to Analysis of the Infinite. Springer-Verlag, Berlin. https://doi.org/10.1007/978-1-4612-1021-4
- Chebyshev, P.L. (1946) Selected Mathematical Works. Gostekhizdat, Moscow. [In Russian]
- Riemann, G.F.B. (1972) On the Number of Prime Numbers Less than a Given Quantity. Chelsea, New York.
- Titchmarsh, E.C. (1986) The Theory of the Riemann Zeta Function. 2nd Revised (Heath-Brown) Edition, Oxford University Press, Oxford.
- Ray, D. and Singer, I.M. (1971) R-Torsion and the Laplacian on Riemannian Manifolds. Advances in Mathematics, 7, 145-210. https://doi.org/10.1016/0001-8708(71)90045-4
- Bost, J.-B. (1987) Fibres determinants, determinants regularises et measures sur les espaces de modules des courbes complexes. Séminaire Bourbaki, 152-153, 113-149.
- Kawagoe, K., Wakayama, M. and Yamasaki, Y. (2008) The q-Analogues of the Riemann zeta, Dirichlet L-Functions, and a Crystal Zeta-Function. Forum Mathematicum, 20, 126. https://doi.org/10.1515/FORUM.2008.001
- Müntz, Ch.H. (1992) Beziehungen der Riemannschen ζ-Funktion zu willkurlichen reellen Funktionen. Matematisk Tidsskrift. B, 39-47.
- Baibekov, S.N. and Durmagambetov. A.A. (2016) Infinitely Many Twin Primes. arXiv:1609.04646 [math.GM]