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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
##### Keywords:
$$L$$-functions; critical line; zeros
Full Text:
##### References:
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