We discuss how one could study asymptotics of cyclotomic quantities via the mean values of certain multiplicative functions and their Dirichlet series using a theorem of Delange. We show how this could provide a new approach to Artin's conjecture on primitive roots. We focus on whether a fixed prime […]

For a positive integer n and a real number α, the generalized Laguerre polynomials are defined by L (α) n (x) = n j=0 (n + α)(n − 1 + α) · · · (j + 1 + α)(−x) j j!(n − j)!. These orthogonal polynomials are solutions to Laguerre's Differential Equation which arises in the treatment of the harmonic […]

We give a short survey of some recent remarkable advances on the twin prime problem. Beginning with the breakthrough work of Zhang in May 2013, we trace the developments culminating in the work of Maynard and Tao in November 2013 that led to simplifications and numerical improvements of Zhang's […]