A Central Limit Theorem for Linear Combinations of Logarithms of Dirichlet $L$-functions Sampled at the Zeros of the Zeta Function

Fatma Çiçek, Steven M. Gonek, Scott J. Kirila

Let $L(s,{\chi }_1),\dots ,L(s,{\chi }_N)$ be primitive Dirichlet $L$-functions different from the Riemann zeta function. Under suitable hypotheses we prove that any linear combination $a_…