Timeline for When does one quadratic form divide another?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2019 at 23:23 | comment | added | Will Sawin | Maybe one can try the (Kloosterman?) circle method for the full problem but I am not optimistic. | |
| Nov 29, 2019 at 23:23 | comment | added | Will Sawin | In the $Q_1$ definite case, it seems that $Q_2 - c Q_1 =0 $ has solutions for only finitely many $c$, and we can solve one $c$ at a time, which is just a single quadratic form in four variables. I think estimating the number of solutions by the circle method is a classically solved problem. So in fact we may assume $Q_1$ indefinite. I think the number of solutions to the previous problem provides a lower bound, but should maybe be off by a log factor because of the sum over $c$ (just thinking heuristically). | |
| Nov 29, 2019 at 22:48 | comment | added | Stanley Yao Xiao | @LSpice I liked your edit, and I made a further refinement. | |
| Nov 29, 2019 at 22:40 | history | edited | Stanley Yao Xiao | CC BY-SA 4.0 |
added 10 characters in body
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| Nov 29, 2019 at 22:40 | comment | added | Stanley Yao Xiao | @NoamD.Elkies in my question one cannot assume that $Q_1$ is definite. | |
| Nov 29, 2019 at 2:42 | comment | added | WhatsUp | Why starting with $4$ variables? What can be said about e.g. quadratic forms of $2$ variables? | |
| Nov 29, 2019 at 2:36 | comment | added | LSpice | (Also, the title seems quite different from the actual question, which seems to be more like "how often do the values of one quadratic form divide the values of another?") | |
| Nov 29, 2019 at 2:36 | comment | added | LSpice | At least for me, it was hard to see what this question had to do about divisibility, since the condition on the values of $Q_1$ and $Q_2$ was way off to the right. I edited to make it more prominent, hopefully without disturbing meaning. Please feel free to revert if you disagree. | |
| Nov 29, 2019 at 2:35 | history | edited | LSpice | CC BY-SA 4.0 |
Changed display environment
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| Nov 29, 2019 at 1:53 | comment | added | Noam D. Elkies | Is $Q_1$ definite or indefinite? (For $Q_2$ it's less of an issue, because the question for $Q_2 - c Q_1$ is equivalent to the one for $Q_2$ and might have a different signature.) | |
| Nov 29, 2019 at 1:44 | history | asked | Stanley Yao Xiao | CC BY-SA 4.0 |