Analytic properties of arithmetic zeta functions and geometric symmetry

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Zeta functions are a group of certain special functions having its origin in the Riemann zeta function. They play important roles in various fields of mathematics. In this research project, we studied about important analytic properties of arithmetic zeta functions like analytic continuations and distributions of thier poles and zeros. As the results, we established a new bridge between analytic properties of zeta functions in number theory and modern harmonic analysis, and obtained new results on the distribution of zeros of so-called high-rank zeta functions which are direct generalizations of the Riemann zeta function.