Timeline for Transcendence of products of certain real algebraic numbers
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| May 19, 2015 at 16:29 | answer | added | Valborg | timeline score: 3 | |
| Jan 23, 2015 at 14:59 | comment | added | Geoff Robinson | Similar infinite products can even be rational: For example, $\prod_{i=1}^{\infty} \frac{p_{i}^{2}+1}{p_{i}^{2}-1} = \frac{5}{2},$ where $p_{i}$ is the $i$-th prime. | |
| Jan 23, 2015 at 14:59 | comment | added | Gerald Edgar | $\prod_{n=1}^\infty n^{1/n^2} = \exp(-\zeta'(2))$, so show that is transcendental! | |
| Jan 23, 2015 at 14:47 | comment | added | Bobby Grizzard | @Gerald if that is easier, that would be interesting as well. For whatever reason, it seemed easier for me to think about when things were relatively prime. | |
| Jan 23, 2015 at 14:30 | comment | added | Gerald Edgar | By the way, what about the (presumably) easier case $\prod_{n=1}^\infty n^{1/n^2}$ ?? | |
| Jan 23, 2015 at 14:29 | comment | added | Gerald Edgar | My sense: A proof that this is rational would be interesting. A proof that this is transcendental would be very interesting. A proof that this is algebraic but irrational would be stupendous. | |
| Jan 23, 2015 at 12:26 | history | edited | Bobby Grizzard | CC BY-SA 3.0 |
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| Jan 23, 2015 at 12:16 | comment | added | Bobby Grizzard | @Hjalmar not that I know of! I had a vague idea about a possible novel way to show that some numbers of this form are transcendental. Before I spent too long figuring out if this idea worked, I wanted to get a sense of whether or not anything could be said already. | |
| Jan 23, 2015 at 8:09 | comment | added | Hjalmar Rosengren | I haven't downvoted this but it would be good to see some indication where the question comes from. Does the number $z$ appear naturally in any context? | |
| Jan 23, 2015 at 2:48 | comment | added | Bobby Grizzard | This question has received two downvotes. I would greatly appreciate any feedback on why this question is inappropriate for MO. | |
| Jan 22, 2015 at 17:17 | history | edited | Bobby Grizzard |
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| Jan 22, 2015 at 16:50 | history | asked | Bobby Grizzard | CC BY-SA 3.0 |