Geodesic
On the zeros of the Davenport--Heilbronn function
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 72-94

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Let $N_0(T)$ be the number of zeros of the Davenport–Heilbronn function in the interval $[1/2,1/2+iT]$. It is proved that $N_0(T)\gg T(\ln T)^{1/2+1/16-\varepsilon }$, where $\varepsilon $ is an arbitrarily small positive number. 
@article{TRSPY_2017_296_a5,
     author = {S. A. Gritsenko},
     title = {On the zeros of the {Davenport--Heilbronn} function},
     journal = {Informatics and Automation},
     pages = {72--94},
     publisher = {mathdoc},
     volume = {296},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a5/}
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S. A. Gritsenko. On the zeros of the Davenport--Heilbronn function. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 72-94. http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a5/