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We consider the joint value distribution of Dirichlet $L$-functions in thecritical strip $\frac{1}{2} < \sigma < 1$. We show that the values of distinctDirichlet $L$-functions are dependent in the sense that they do not behave likeindependently distributed random variables and they prevent each other fromobtaining large values. Nevertheless, we show that distinct Dirichlet$L$-functions can achieve large values simultaneously infinitely often.

Simultaneous large values and dependence of Dirichlet $L$-functions in the critical strip