A variant of Bombieri-Vinogradov theorem with explicit constants
  In this paper we improve the result of Akbary and Hambrook by a factor of log x by obtaining a better version of Vaughan's inequality and using the explicit variant of an inequality connected to the M\"obius function, derived by Helfgott in his work on ternary Goldbach conjecture. 
Alisa Sedunova
math.NT