Geodesic
On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach
Izvestiya. Mathematics , Tome 80 (2016) no. 3, pp. 602-622

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We consider in detail Selberg's method for proving that under certain natural assumptions, a positive proportion of the non-trivial zeros of a linear combination of L-functions from the Selberg class lie on the critical line. As an example, we provide all the ingredients necessary to prove this result in the case of a linear combination of L-functions of degree two attached to automorphic forms.
Keywords: Riemann hypothesis, zeros on the critical line, Selberg class, density theorems, Hecke L-functions. 
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     author = {I. S. Rezvyakova},
     title = {On the zeros of linear combinations of {L-functions} of degree two on the critical line. {Selberg's} approach},
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I. S. Rezvyakova. On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach. Izvestiya. Mathematics , Tome 80 (2016) no. 3, pp. 602-622. http://geodesic.mathdoc.fr/item/IM2_2016_80_3_a7/