Geodesic
Lower Bounds for Positive and Negative Parts of Measures and the Arrangement of Singularities of Their Laplace Transforms
Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 84-98.

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For a real measure with variation $V(x)$ satisfying the estimate $V(x)\le c_0\exp(Cx)$ and with the Laplace transform holomorphic in the disk $\{|s-C|\le C\}$ and having at least one pole of order $m$, we obtain lower bounds for the positive and negative parts of the measure $V_\pm(x)>cx^m$, $x>x_0$. We establish lower bounds for $V_\pm(x)$ on “short” intervals. Applications to number theory of the results obtained are considered.
Keywords: real measure, positive and negative parts of a measure, analytic function, pole of a meromorphic function, Möbius function, Riemann zeta function.
Mots-clés : Laplace transform 
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A. Yu. Popov; A. P. Solodov. Lower Bounds for Positive and Negative Parts of Measures and the Arrangement of Singularities of Their Laplace Transforms. Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 84-98. http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a9/

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