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- W4297411700 abstract "For a real number $k$, define $pi_k(x) = sum_{ple x} p^k$. When $k>0$, we prove that $$ pi_k(x) - pi(x^{k+1}) = Omega_{pm}left(frac{x^{frac12+k}}{log x} logloglog xright) $$ as $xtoinfty$, and we prove a similar result when $-1<k<0$. This strengthens a result in a paper by J. Gerard and the author and it corrects a flaw in a proof in that paper. We also quantify the observation from that paper that $pi_k(x) - pi(x^{k+1})$ is usually negative when $k>0$ and usually positive when $-1<k<0$." @default.
- W4297411700 created "2022-09-28" @default.
- W4297411700 creator A5067692123 @default.
- W4297411700 date "2022-09-21" @default.
- W4297411700 modified "2023-09-24" @default.
- W4297411700 title "Sums of Powers of Primes II" @default.
- W4297411700 doi "https://doi.org/10.48550/arxiv.2209.12845" @default.
- W4297411700 hasPublicationYear "2022" @default.
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