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Staff Introduction

TRINH, Khanh Duy / Assistant Professor

My research concerns with applications of probability theory to number theory. In particular, I am interested in using probabilistic tools to study general Dirichlet series and the Riemann zeta function, two of number theory's main objects. Recently, I found a suitable compactification of the real line to study value distributions of general Dirichlet series. From this, limit distributions of general Dirichlet series are well identified. My purpose is to apply this compactification method to obtain new limit theorems. Particularly, some main problems I want to study are: (1) Besicovitch almost periodic functions with spectrum on Dirichlet sequence, value distributions of general Dirichlet series and their relation (2) the behavior of limit distributions of general Dirichlet series near and on the critical line and (3) random matrix theory and its applications to investigate zero-distribution and moment problem of the Riemann zeta function.

Keywords Probability Theory, Analytic Number Theory, General Dirichlet Series, Besicovitch Almost Periodic Functions, Random Matrix Theory
Faculty , Department Institute of Mathematics for Industry , Fundamental Mathematics