Product of Dirichlet $L$-functions - sign changes of $S(t;\chi_{1},\chi_{2})$

Let $\chi_{1}, \chi_{2}$ be two primitive Dirichlet characters with fixed moduli, and let
$$ S(t;\chi_{1},\chi_{2})\,=\,\frac{1}{\pi}\text{arg}\biggl(L\bigl(\tfrac{1}{2}+it,\chi_{1}\bigr)L\bigl(\tfrac{1}{2}+it,\chi_{2}\bigr)\biggr) $$
be an argument of the product of the corresponding $L$-functions on the critical line. In the talk, some new results concerning the behavior of $S(t;\chi_{1},\chi_{2})$ are introduced: formulas for moments, the distribution function and lower bound for the number of sign changes on given interval.

^* Conference identificator: 947 3270 9056 Password: 555834