Let $\alpha>0$ and $A>0$. Suppose that $$R(X)=\int_{1}^{X}L(t)t^{-\alpha}\,dt,\,\,X>1$$ satisfies $\lim_{X\to\infty}R(X)=-A$. Then $L(t)<0$ for all $t$ sufficiently large.
Is it true?
2026-03-31 13:49:30.1774964970
Sign of a function inside of an integral obtained from the asymptotic behavior of the integral
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