Timeline for Distinct exponents in the factorization of the factorial, a problem of Erdős
Current License: CC BY-SA 4.0
7 events
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| Jan 8, 2022 at 8:25 | vote | accept | sebaztian | ||
| Jan 7, 2022 at 21:48 | comment | added | Terry Tao | Most likely a sufficiently uniform version of the k-tuple conjecture would imply an averaged version of the asymptotic where one averages $h(n)$ on intervals such as $[x,x+x^{1/2+\varepsilon}]$. By the way, to get an asymptotic for the expected number of pairs of primes in intervals of order $\log X$ requires something like RH + a sufficiently strong pair correlation conjecture: see ams.org/journals/tran/2017-369-06/S0002-9947-2016-06835-X | |
| Jan 7, 2022 at 18:38 | comment | added | Will Sawin | @SylvainJULIEN The $k$-tuple conjecture as stated, or a uniform version of it, might not be sufficient as $k$-tuples that cross the boundaries of these intervals need to be treated differently, but the needed result is certainly in the same ballpark. | |
| Jan 7, 2022 at 18:36 | history | edited | Will Sawin | CC BY-SA 4.0 |
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| Jan 7, 2022 at 18:26 | comment | added | Sylvain JULIEN | By the way, wouldn't Hardy-Littlewood's $k$-tuple conjecture provide the sought after symptotics? | |
| Jan 7, 2022 at 17:47 | history | edited | Will Sawin | CC BY-SA 4.0 |
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| Jan 7, 2022 at 16:12 | history | answered | Will Sawin | CC BY-SA 4.0 |