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Recently, we have established and used the generalized Littlewood theoremconcerning contour integrals of the logarithm of analytical function to obtaina few new criteria equivalent to the Riemann hypothesis. Here, the same theoremis applied to calculate certain infinite sums and study the properties ofzeroes of a few analytical functions.

On the use of the generalized Littlewood theorem concerning integrals of  the logarithm of analytical functions for calculations of infinite sums and  analysis of zeroes of analytical functions