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- W2792654811 abstract "Let us denote by (pi (x)) the number of primes (leqslant x), by ({{mathrm{li}}}(x)) the logarithmic integral of x, by (theta (x)=sum _{pleqslant x} log p) the Chebyshev function and let us set (A(x)={{mathrm{li}}}(theta (x))-pi (x)). Revisiting a result of Ramanujan, we prove that the assertion “(A(x) > 0) for (xgeqslant 11)” is equivalent to the Riemann Hypothesis." @default.
- W2792654811 created "2018-03-29" @default.
- W2792654811 creator A5066069531 @default.
- W2792654811 date "2017-01-01" @default.
- W2792654811 modified "2023-09-25" @default.
- W2792654811 title "Estimates of $${{mathrm{li}}}(theta (x))-pi (x)$$ and the Riemann Hypothesis" @default.
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- W2792654811 doi "https://doi.org/10.1007/978-3-319-68376-8_32" @default.
- W2792654811 hasPublicationYear "2017" @default.
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