Timeline for Why is it hard to prove that the Euler Mascheroni constant is irrational?
Current License: CC BY-SA 3.0
10 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| May 9, 2013 at 1:07 | vote | accept | user16557 | ||
| May 4, 2013 at 20:33 | comment | added | Brian Rushton | Does this mean the Oiled-Macaroni constant is a renormalized feta function? Mmm... Greek food... | |
| May 4, 2013 at 20:04 | history | edited | Douglas Zare | CC BY-SA 3.0 |
corrected statement about periods
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| May 4, 2013 at 19:47 | comment | added | Douglas Zare | @quid I was using the wrong definition of period, not trying to claim something new. | |
| May 4, 2013 at 18:52 | comment | added | user9072 | You claim e known to be a period; AFAIK, but I might be wrong, this is neither known (nor much conjectured). Could you please provide a reference for this claim. Thanks in advance. | |
| May 3, 2013 at 5:25 | comment | added | Nilotpal Kanti Sinha | "There are a lot more connections known between π and e and other numbers than between γ and other numbers." This may not entirely true. The numbers $e^{\gamma}$ pops up every now and then in the theory of primes. For example Merten's Theorems, Cramer-Granville's conjecture etc to name a few. But I do agree that the connection between $\gamma$ and other numbers that has nothing to do with primes directly or indirectly is far less common. | |
| May 2, 2013 at 22:32 | comment | added | KConrad | For a general number field $K$, Ihara introduced in 2006 an Euler-Kronecker constant $\gamma_K$, which is best defined from the Laurent expansion at $s=1$ not of $\zeta_K(s)$, but rather of $\zeta_K'(s)/\zeta_K(s)$: $\zeta_K'(s)/\zeta_K(s) = -1/(s-1) + \gamma_K + O(s-1)$. In terms of the Laurent expansion $\zeta_K(s) = R/(s-1) + c + O(s-1)$, we have $\gamma_K = c/R$. For $K = {\mathbf Q}$, $R = 1$ and therefore $c = \gamma_{\mathbf Q}$. But for general $K$ the number $R$ is not 1 and the constant term of $\zeta_K(s)$ at $s = 1$ is the "wrong" object of interest. | |
| May 2, 2013 at 13:46 | comment | added | Noam D. Elkies | Note, though, that the fact that $\gamma$ is not known to be a "period" does not exclude an irrationality proof from some other direction; the irrationality of numbers such as $\log_2 3$ is even easier to prove than the irrationality of $\pi$, and $\log_2(3)$ is not expected to be a period (though it's the ratio of the periods $\log 3$ and $\log 2$). | |
| May 2, 2013 at 3:15 | history | answered | Douglas Zare | CC BY-SA 3.0 |