Timeline for Simplifying a sum in terms of divisor function Cauchy products
Current License: CC BY-SA 3.0
8 events
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| Feb 23, 2014 at 4:01 | history | edited | Alexey Ustinov | CC BY-SA 3.0 |
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| Feb 23, 2014 at 3:55 | comment | added | Ethan Splaver | Sorry, I forgot to tell you I actually did find a closed form in the last 2 hours using a combinatoral identity and some other techniques. It turns out that: $$\sum_{ax+by=n}_{(a,x,b,y)\in \mathbb{N^4}}\max{\{a,b\}}=nd(n)-\sigma_2(n)+2\sum_{k=1}^{n-1}d(k)\sigma(n-k)$$ | |
| Feb 23, 2014 at 3:47 | comment | added | Alexey Ustinov | It will be great if you'll find closed form for such sums. The binary additive divisor problem (see Motohashi, Y. The binary additive divisor problem Ann. Sci. École Norm. Sup. (4), 1994, 27, 529-572) looks more simple but we don't have closed form for it. | |
| Feb 23, 2014 at 2:07 | history | edited | darij grinberg | CC BY-SA 3.0 |
added 114 characters in body
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| Feb 23, 2014 at 0:23 | comment | added | Ethan Splaver | I can't seem to find the result, they seem to be proving asymptotics for convolutions of divisor functions. I was hoping there was a closed form for $\sum_{ax+by=n}_{(a,x,b,y)\in \mathbb{N^4}} \max(a,b)$ | |
| Feb 22, 2014 at 10:30 | comment | added | Alexey Ustinov | Give me your e-mail [email protected] | |
| Feb 22, 2014 at 8:05 | comment | added | Ethan Splaver | Do you have a subscription to the journal or do you know where I can get the pdf? I can't afford the $38 to view the article for one day. | |
| Feb 22, 2014 at 6:42 | history | answered | Alexey Ustinov | CC BY-SA 3.0 |