BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, ON A PROPERTY OF RIEMANN ZETA FUNCTION // BSU Bulletin. Mathematics, Informatics. - 2022. №2. . - С. 3-10.
Title:
ON A PROPERTY OF RIEMANN ZETA FUNCTION
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Annotation:
The Riemann zeta function and his famous conjecture regarding the property of this function were presented in his 1859 paper, which was concerned about the distribution of prime numbers. In this article, we will prove some properties of Riemann zeta function and based on those results we will formulate Theorem. An exposition is given, partly historical and partly mathematical, of the Riemann zeta function and the associated Riemann hypothesis. Relevance of these investigations to the theory of the distribution of prime numbers is discussed.
Keywords:
Riemann zeta function, Chebyshev’s conjecture and the Chebyshev functions, gamma function.
List of references:
Titchmarsh E.C. The Theory of the Riemann Zeta-function. Oxford Uni- versity Press, 1986. 418 p.
Kudryavtseva E., Saidak F., Zvengrowski P. Riemann and his zeta func- tion. Morfismos. 2005. Vol. 9, No. 2. Pp. 1–48.
Iwaniec H. Lectures on the Riemann Zeta Function. American Mathemat- ical Society, University Lecture Series. 2014. Vol. 62. 119 p.
Kobayashi S. Mathematicians Who Lost Their Faces: Essays in Idleness on Mathematics (in Japanese). Iwanami Publisher, Tokyo, 2013. Pp. 40– 42.
Kudryavtseva E., Saidak F., Zvengrowski P. Riemann and his zeta func- tion. Morfismos. 2005. Vol. 9, No. 2. Pp. 1–48.
Iwaniec H. Lectures on the Riemann Zeta Function. American Mathemat- ical Society, University Lecture Series. 2014. Vol. 62. 119 p.
Kobayashi S. Mathematicians Who Lost Their Faces: Essays in Idleness on Mathematics (in Japanese). Iwanami Publisher, Tokyo, 2013. Pp. 40– 42.
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