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- W4300986221 abstract "We establish the optimal order of Malliavin-type remainders in the asymptotic density approximation formula for Beurling generalized integers. Given $alphain (0,1]$ and $c>0$ (with $cleq 1$ if $alpha=1$), a generalized number system is constructed with Riemann prime counting function $ Pi(x)= operatorname*{Li}(x)+ O(xexp (-c log^{alpha} x ) +log_{2}x), $ and whose integer counting function satisfies the extremal oscillation estimate $N(x)=rho x + Omega_{pm}(xexp(- c'(log xlog_{2} x)^{frac{alpha}{alpha+1}})$ for any $c'>(c(alpha+1))^{frac{1}{alpha+1}}$, where $rho>0$ is its asymptotic density. In particular, this improves and extends upon the earlier work [Adv. Math. 370 (2020), Article 107240]." @default.
- W4300986221 created "2022-10-04" @default.
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- W4300986221 date "2021-09-17" @default.
- W4300986221 modified "2023-10-16" @default.
- W4300986221 title "The optimal Malliavin-type remainder for Beurling generalized integers" @default.
- W4300986221 doi "https://doi.org/10.48550/arxiv.2109.08509" @default.
- W4300986221 hasPublicationYear "2021" @default.
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