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On the zeros of linear combinations of $$L$$-functions of degree two on the critical line. Selberg’s approach. (English. Russian original) Zbl 1350.11083
Izv. Math. 80, No. 3, 602-622 (2016); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 80, No. 3, 151-172 (2016).
Define a linear combination of $$m$$ distinct Hecke $$L$$-functions $$L_j(s)$$ attached to complex characters on the ideal group, $$j=1,\dots,m$$, by $F(s)=\sum_{j=1}^{m}c_j L_j(s), \quad c_j \in \mathbb R.$
In this paper, it is shown that on the interval $$\{s=\frac{1}{2}+it, T \leq t\leq 2T\}$$, for the number of zeros $$N_0(T)$$ of the function $$F(s)$$, the following estimate holds $N_0(T) \gg \frac{1}{m}T \log T.$

##### MSC:
 11M41 Other Dirichlet series and zeta functions 11M26 Nonreal zeros of $$\zeta (s)$$ and $$L(s, \chi)$$; Riemann and other hypotheses
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