Geodesic
On a Problem of Karatsuba
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 517-528

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We obtain lower bounds for the fractional moments of linear combinations of analogs of the Hardy function. In addition, we apply these estimates to the Karatsuba problem of finding a lower bound for the number of zeros of the linear combination of analogs of Hardy functions on the interval $(0,T]$.
Keywords: Hardy function, Dirichlet character, Euler function, fractional moments of the Hardy function, Stirling's formula, Cauchy's theorem, Dirichlet $L$-function. 
@article{MZM_2010_88_4_a3,
     author = {S. A. Gritsenko},
     title = {On a {Problem} of {Karatsuba}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {517--528},
     publisher = {mathdoc},
     volume = {88},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a3/}
}
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S. A. Gritsenko. On a Problem of Karatsuba. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 517-528. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a3/