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Selberg’s method in the problem about the zeros of linear combinations of \(L\)-functions on the critical line. (English. Russian original) Zbl 1392.11064
Dokl. Math. 92, No. 1, 448-451 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 463, No. 3, 270-273 (2015).
Summary: In the late 1990s, Atle Selberg invented a new method, which had allowed him to prove that if a linear combination of Dirichlet \(L\)-functions satisfies a functional equation, then a positive proportion of its zeros lie on the critical line. The paper considers this method in detail for the general case of a linear combination of \(L\)-functions from the Selberg class and applies it to a linear combination of \(L\)-functions from the Selberg class of degree 2.

MSC:
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
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References:
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