5 May
2011
5 May
'11
9:09 a.m.
It's amazing how this issue has resisted progress until 1979. Many finite sets of zeta(odd)'s are now known to contain at least one irrational (e.g., papers by W. Zudilin). But I'd be more interested to know whether zeta(n)/pi^n is rational for n odd, as it is for n even. --Dan Rich writes [of an attempt to show zeta(5) is irrational]: << The paper is only 7 pages, and uses techniques similar to the proof in Hardy & Wright that pi is irrational. It's more complicated of course. There's quite a bit of stuff to check, some quintuple integrals, etc. The author claims he has proof of irrationality of zeta(odd) at the end of the paper.
Sometimes the brain has a mind of its own.