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 Publish in OALib Journal ISSN: 2333-9721 APC: Only $99  Views Downloads  Relative Articles Estimates of convolutions of certain number-theoretic error terms Convolutions and mean square estimates of certain number-theoretic error terms Inconsistency of Measure-Theoretic Probability Prequential probability: game-theoretic = measure theoretic Measure Theoretic Trigonometric Functions Nonadditive Measure-theoretic Pressure and Applications to Dimensions of an Ergodic Measure On a measure theoretic area formula Unequal Error Protection: An Information Theoretic Perspective Quantum field theoretic approach to neutrino oscillations in matter Measure-theoretic rigidity for Mumford curves More... Mathematics 2015 # Measure Theoretic Aspects of Oscillations of Error Terms  Full-Text Cite this paper Abstract: In this paper we obtain$\Omega$and$\Omega_\pm$estimates for a wide class of error terms$\Delta(x)$appearing in Perron summation formula. We revisit some classical$\Omega$and$\Omega_{\pm}$bounds on$\Delta(x)$, and obtain$\Omegabounds for Lebesgue measure of the following types of sets: \begin{align*} \A_+&:=\{T\leq x \leq 2T: \Delta(x)> \lambda x^{\alpha}\},\\ \A_-&:=\{T\leq x \leq 2T: \Delta(x)< -\lambda x^{\alpha}\},\\ \A~&:=\{T\leq x \leq 2T: |\Delta(x)|>\lambda x^{\alpha}\}, \end{align*} where\alpha, \lambda>0$. We also prove that if Lebesgue measure of$\A$is$\Omega(T^{1-\delta})$then $\Delta(x)=\Omega_\pm(x^{\alpha-\delta})$ for any$0<\delta<\alpha\$.

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