Timeline for Computing zeta(k), for k odd, using Fourier coefficients
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2019 at 0:29 | comment | added | KConrad | @Puddlestheturtle : while Kevin was correct when he posted his comment in 2009, I suspect he won't want to post new versions of it every 10 years. | |
| Jun 26, 2019 at 23:30 | comment | added | Puddles the turtle | @KevinBuzzard wasn't $1979$ actually $40$ years ago? Respond to this comment in $10$ years. | |
| Jul 5, 2010 at 23:29 | comment | added | Ben Wieland | There was a development in the last 15 years: in 2000, Tanguy Rivoal showed that there are that infinitely many odd irrational zeta values. More precisely, he showed that the dimension of the $\mathbb Q$ vector space spanned by the first $n$ odd zeta values has dimension at least $log(n)$. Applied to the even zeta values, this shows that $\pi$ is transcendental, but the odd zeta values are supposed to be algebraically independent. | |
| Nov 6, 2009 at 13:20 | comment | added | Charles Siegel | Ahh, then I am misremembering what someone told me about how long ago anything was proved, as some googling reveals that it's open if zeta(3) is transcendental. The point of the answer: that we know virtually nothing about zeta(2n+1) stands, though. | |
| Nov 6, 2009 at 12:39 | comment | added | Kevin Buzzard | Apery proved zeta(3) was irrational in 1979: 30 years ago. | |
| Nov 6, 2009 at 11:51 | history | answered | Charles Siegel | CC BY-SA 2.5 |