×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI