A transformation formula with primitive character - Balčiūnas, Aidas (Lietuvos matematikos rinkinys, 2013)
We prove a transformation formula for the exponential sum involving the divisor function, and primitive character modulo q. This formula can be applied to obtain meromorphic continuation for the Mellin transform of the square of Dirichlet L-function with primitive character.
Keywords: Dirichlet $L$-function; Estermann zeta-function; Mellin transform