Timeline for Historical question in analytic number theory
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 5 at 2:47 | history | edited | LSpice | CC BY-SA 4.0 |
Removing spurious line break, while this is on the front page
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| Feb 4 at 18:30 | history | edited | KConrad | CC BY-SA 4.0 |
added 124 characters in body
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| Feb 4 at 17:29 | comment | added | KConrad | @zeynel The paper is "Remarques sur un beau rapport entre les séries des puissances tant directes que réciproques", in Mémoires de l’académie des sciences de Berlin, 17 (1768), pp. 83–106. It can be read at the Euler archive: scholarlycommons.pacific.edu/euler-works/352. That page has a link to the original version as well as an English translation. | |
| Feb 4 at 17:26 | comment | added | KConrad | @zeynel to understand analytic continuation, reading Euler is irrelevant. Euler made free use of divergent series and he did not worry about error bounds. He was not thinking about analytic continuation, which is part of complex analysis, and that is a creation of the 19th century. | |
| Feb 4 at 16:27 | comment | added | zeynel | @NoahSnyder I realize this is very old question but I was trying to find the original paper where Euler extends zeta function to $s>0$ and it seems that your comment is relevant. Do you have a link to that paper in French that you mention? I'm having a hard time understanding the concept of analytic continuation so I thought maybe trying to read original sources may help. Although it may be even more difficult to unedrstand Euler's notation. Thanks | |
| Jun 30, 2018 at 2:46 | comment | added | Noah Snyder | Also this paper is in French instead of Latin, so it’s much more accessible. | |
| Jun 30, 2018 at 2:45 | comment | added | Noah Snyder | Euler also “numerically checked” the equation at one non-integer value $s=3/2$. This part is a bit trickier due to the non-convergence at $s=-1/2. But he rewrote the series so it took longer and longer to start diverging and got a numerical estimate that way. | |
| Jan 29, 2010 at 21:14 | comment | added | Anweshi | Thanks! I always wondered, but was apprehensive of looking into the collected works of Euler. | |
| Jan 29, 2010 at 21:01 | history | answered | KConrad | CC BY-SA 2.5 |