On several problems in analytic number theory

I would like to introduce three projects I am currently working on during my PhD program. They are all connected with the distribution of prime numbers to some extent or to analytic functions which are closely related to this problem. I will give a brief overview of every project, the current result(s) and methods to work through them.
Explicit lower bounds for Dirichlet L-functions.
This is a joint work with my supervisor Tim Trudgian and Mike Mossinghoff. The objective is to refine the result of Louboutin who gives an explicit lower bound for the L-function associated some character $\chi$ at $s=1$ in terms of the conductor of $\chi$ and some constant \lambda which is to be defined during the talk. I will present the main result from the paper and a strategy to get it, as well as the method (nearly complete) to improve it.
Explicit Atkinson formula.
This is a joint work with Aleksander Simonic, a PhD student at UNSW Canberra from our research group. Atkinson provided a formula for the remainder term of the mean value of the Riemann zeta function on the critical line. This appeared to be a useful tool in order to get quite a good upper bound for the remainder term. Atkinson formula contains a non-explicit term $O(\log^2(T))$ depending on some parameter $T.$ Our objective (nearly complete) is to get an explicit term following the work of Atkinson.
Primes in short intervals.
I will shortly introduce the main results around primes in short intervals, present the last result given by Baker, Harman and Pintz and methods/tools which are used in the area.
Conference ID: 942 0186 5629 Password is a six-digit number, the first three digits of which form the number p + 44, and the last three digits are the number q + 63, where p, q is the largest pair of twin primes less than 1000