Abstract:
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.
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