The Zero-density Estimates For Dirichlet L-functrions Near The Line Re S=1

In this paper we suppose that x≥1, y≥0. For any Dirichlet characterχto the modulus q with q≤x, let N(α,χ,y) denote the number of zeros of L(s,χ) in the region In this paper we give the explicit estimation of upper bounds for N(α, q, y) when a is very near to the line Re s= 1.The whole thesis consists of three chapters:In the first chapter, we introduce briefly the development of the Number Theory, and the importance of the zero-density of Dirichlet L-functions. We also give some definitions, notations and the main result of the thesis.The second chapter lists some lemmas and gives the proofs of the Lemmas in order to prove the main result.Chapter three presents the proof of the main result and gives the explicit estimation of upper bounds for N(α, q, y) whenαis very near to the line Re s= 1...