On the mean value of $|L(1, \chi )|^2$ for odd primitive Dirichlet characters

Abstract

Let $f>1$ be given. Whereas a simple formula for the mean value of $|L(1, \chi)|^2$ for odd Dirichlet characters modulo $f$ is known, we explain why there is no hope of ever finding a simple formula for the mean value of $|L(1, \chi)|^2$ for primitive odd Dirichlet characters modulo $f$.