This article is cited in 21 papers

On the zeros of some Dirichlet series lying on the critical line

S. M. Voronin


Abstract: A linear combination of Dirichlet $L$-functions which are known not to have an Euler product is considered. It is proved that the interval
$$ \biggl[\frac12-iT,\frac12+iT\biggr] $$
contains for an arbitrary constant $c>0$ more than $cT$ zeros for $T\to\infty$.
Bibliography: 9 titles.

UDC: 511

MSC: Primary 10H10; Secondary 10H08

Received: 05.06.1979

 English version: Mathematics of the USSR-Izvestiya, 1981, 16:1, 55–82

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