Timeline for A curious property of Ramanujan's function $\tau(n)$
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jan 16, 2016 at 10:20 | comment | added | James Khan | Indeed, the 70 is not ad hoc. They point out in their paper that they have chosen (24,70) precisely because $1^2+2^2+⋯+24^2=70^2$ is what allows the definition of the Leech lattice, which is fundamentally related to $M$ and $j(q)$. | |
| Apr 30, 2015 at 14:47 | comment | added | Tito Piezas III | @Joel: You may be interested in my comment/answer below, in particular, a serendipitous error mentioned in the update. | |
| Apr 30, 2015 at 13:50 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
The correct sign is really positive.
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| Apr 29, 2015 at 16:36 | history | edited | GH from MO |
edited tags
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| Apr 29, 2015 at 16:23 | answer | added | Tito Piezas III | timeline score: 8 | |
| Apr 29, 2015 at 16:12 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Corrected typo (in blue).
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| Oct 31, 2014 at 15:15 | comment | added | Jeremy Rouse | There are some deep mathematics that are related to $\tau(n)$ and $c(n)$ modulo the prime factors of $70$. (For example $\tau(n) \equiv n \sigma_{3}(n) \pmod{7}$.) However, I don't see a way to translate these facts into the two congruences that were stated in this paper. | |
| Oct 31, 2014 at 14:50 | comment | added | Zurab Silagadze | The combination (24,70) is somewhat unique. See mathworld.wolfram.com/CannonballProblem.html | |
| Oct 31, 2014 at 14:41 | comment | added | Zurab Silagadze | "the number 70, which is chosen a bit ad hoc" -- but how about $1^2+2^2+\cdots+24^2=70^2$? | |
| Oct 31, 2014 at 14:11 | comment | added | Joël | "42 is the Answer to the Ultimate Question of Life, the Universe and Everything. This Answer was first calculated by the supercomputer Deep Thought after seven and a half million years of thought. This shocking answer resulted in the construction of an even larger supercomputer, named Earth, which was tasked with determining what the question was in the first place." | |
| Oct 31, 2014 at 14:05 | comment | added | Per Alexandersson | Sure, but you have one degree of freedom (or two, if you count the upper number in the sum), namely the number 70, which is chosen a bit ad hoc. So, 70 is chosen such that both numbers agree... | |
| Oct 31, 2014 at 12:58 | comment | added | Zurab Silagadze | Right. But the same number appears in the second statement indicating, perhaps, that 42 should have some meaning and is not merely an accident. | |
| Oct 31, 2014 at 11:32 | comment | added | Per Alexandersson | In the first statement, this is just a fixed sum, right? So, it must be some number, which happens to be 42... | |
| Oct 31, 2014 at 10:23 | history | asked | Zurab Silagadze | CC BY-SA 3.0 |