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I am reading an article "Transcendental equations satisfied by the individual zeros of Riemann $\zeta$, Dirichlet and modular L-functions" by G. Franca and A. LeClair (2015) see here. The ...

Let $\chi$ be a Dirichlet character mod $q$ and $\Lambda(n)$ be the von Mangoldt function. Let $c(\chi)=1$ if $\chi$ is the principal character, and zero otherwise. Let $\Theta_\chi$ be the supremum ...

Let $L_i(s)$ be some $L$-functions. (I am interested in the case when $L_1, L_2$ are two different Hecke $L$-function associated to the same number field.) Let $$F(s)=\int_{\Re w=\sigma} \frac{1}{w} ...