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Riemann Zeta Function and Its Applications
- 1 Department of Mathematics and Physics, Xi’an Jiangtong-Liverpool University, Suzhou 215123, China
- 2 Department of Mathematics and Applied mathematics, Chongqing University, Chongqing 400044, China
* Author to whom correspondence should be addressed.
Abstract
This paper focuses on the introduction and proof of the fundamental properties of ζ(z), i.e. Riemann zeta function and explores its applications in algebra. We begin with a systematic derivation and proof of the basic characteristics of the zeta function. Following this, we examine its application in algebra, including the use of the Dirichlet L-function to prove Dirichlet’s theorem. Furthermore, we show the classical result for the subgroup growth rate of J-groups and the enumeration of n-dimensional irreducible representations of Heisenberg groups.
Keywords
Riemann’s zeta function, number theory, group zeta function.
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Cite this article
Shi,Y.;Lin,Z. (2024). Riemann Zeta Function and Its Applications. Theoretical and Natural Science,53,191-202.
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Volume title: Proceedings of the 2nd International Conference on Applied Physics and Mathematical Modeling
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