Zeros of L functions and distribution of primes

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While the study of prime numbers is an antique field of study, it is only recently that powerful tools have been developed to bring answers to century old questions. One of the main tools is the interplay between the primes and the zeros of the complex valued Riemann zeta function. The Riemann Hypothesis, a 150 year old conjecture, asserts that all its nontrivial zeros lie on the vertical 1/2-line. My research investigates the location and density of the zeros of the zeta function (and other L-functions) and the distribution of primes. It also has an explicit flavor which has become increasingly relevant. For instance, important work by Tao and Helfgott related to Goldbach's conjecture and other work by Hough solving Erdos covering congruences conjecture rely on explicit results about the primes. Moreover my results can be directly applied in other fields, such as Diophantine approximation, cryptography, and computer science.