Geodesic
On the zeros of a special type of function connected with Dirichlet series
Izvestiya. Mathematics , Tome 38 (1992) no. 3, pp. 471-502

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Theorems are proved on the number of zeros of linear combinations of Dirichlet $L$-functions that lie on intervals of the critical line. 
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     author = {A. A. Karatsuba},
     title = {On the zeros of a special type of function connected with {Dirichlet} series},
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A. A. Karatsuba. On the zeros of a special type of function connected with Dirichlet series. Izvestiya. Mathematics , Tome 38 (1992) no. 3, pp. 471-502. http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a2/