Timeline for Asymptotics of $\vartheta(x+y)-\vartheta(x)$, where $\vartheta$ is the Chebyshev function, when $y\in[x^\alpha, x]$ for some $\alpha\in(0,1)$
Current License: CC BY-SA 4.0
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| Mar 7 at 17:58 | history | edited | Maximilian Janisch | CC BY-SA 4.0 |
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| Mar 7 at 17:54 | comment | added | Maximilian Janisch | @AnuragSahay Thank you for the pointer towards Baker--Harman--Pintz! I am interested in asymptotics, so I guess stopping at Heath-Brown is all I can do. Also thanks for your second comment, in principle I agree with you, but I think it is not very important if we write out the initials or not. | |
| Mar 7 at 16:27 | comment | added | Anurag Sahay | A complete aside by the way: if Heath-Brown wanted to be cited with his full name, he probably wouldn't use initials for the majority (all?) his papers. I think it's usually best to defer to the name format that actually appears in the publication when citing. | |
| Mar 7 at 11:37 | history | edited | Maximilian Janisch | CC BY-SA 4.0 |
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| Mar 6 at 13:57 | history | edited | Maximilian Janisch | CC BY-SA 4.0 |
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| Mar 6 at 0:20 | comment | added | GH from MO | Please use a high-level tag like "nt.number-theory". I added this tag now. Regarding high-level tags, see meta.mathoverflow.net/questions/1075/… | |
| Mar 6 at 0:20 | history | edited | GH from MO |
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| Mar 5 at 23:05 | history | edited | Maximilian Janisch | CC BY-SA 4.0 |
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| Mar 5 at 21:37 | comment | added | Anurag Sahay | I think if you really want an asymptotic then Heath-Brown's result is the best there is. If you are happy with a lower bound on $\vartheta(x + y) - \vartheta(x)$ of the right order of magnitude then many people (Heath-Brown, Iwaniec, Baker, ...) have worked on this problem, and the best result is due to Baker--Harman--Pintz from 2001, where they showed that $\alpha = 0.525$ works. | |
| Mar 5 at 20:07 | history | asked | Maximilian Janisch | CC BY-SA 4.0 |