Timeline for Number of integer partitions modulo 3
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2019 at 9:58 | vote | accept | Martin Rubey | ||
| Feb 16, 2019 at 20:05 | comment | added | Martin Rubey | Unfortunately, my package requires that the coefficients live in a field. However, I checked all primes below $20$, and found equations for all of them with the exception of the prime $2$. I guess that for larger primes the differential equation in mathoverflow.net/a/47706 should be non-degenerate. | |
| Feb 16, 2019 at 19:12 | comment | added | Somos | @FedorPetrov Okay, I got some modulo 8 results. Let $f:=f(x), f_1:=f'(x), f_2:=f''(x),f_3:=f'''(x).$ Then $6 f f_1^3 +3f^2 f_1 f_2 + 3 f^3 f_3 + 2x f_1^4 + x f^2 f_2^2 \equiv 0 \pmod 8$ based on a 4th degree 4-section identity. | |
| Feb 16, 2019 at 18:11 | comment | added | Somos | @FedorPetrov I am not surprised at the modulo 2 problem. It has to do with modular functions I think. You may be correct about modulo 4 though. I am not sure. | |
| Feb 16, 2019 at 18:06 | comment | added | Fedor Petrov | as I understood from OP, there are difficulties already with differential equation modulo 2. On the other hand, it may appear, say, that there exists a non-trivial relation modulo 4 which is trivial modulo 2. | |
| Feb 16, 2019 at 17:52 | comment | added | Somos | @FedorPetrov Good question!! I had not considered differential equation power series modulo primes before which is why the original question confused me. However, based on my experience with other kinds of congruences between power series I would not be surprised. For example, $ \theta_3^4(q) = \theta_4^4(q) + \theta_2^4(q)$ and $\theta_2^4(q) \equiv 0 \pmod {16}$ | |
| Feb 16, 2019 at 17:35 | comment | added | Fedor Petrov | Very interesting! Do other relations in your essay also produce differential equations modulo other primes? | |
| Feb 16, 2019 at 17:29 | history | edited | Somos | CC BY-SA 4.0 |
Fixed a typo. Reword.
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| Feb 16, 2019 at 15:00 | history | edited | Somos | CC BY-SA 4.0 |
Replace q->x for A(),B(),C()
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| Feb 16, 2019 at 14:41 | history | answered | Somos | CC BY-SA 4.0 |