Timeline for Which quaternary quadratic form represents $n$ the greatest number of times?
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13 events
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| Dec 12, 2016 at 18:11 | comment | added | Will Jagy | @WillSawin just sent an email to your princeton.edu address. Just two text files, one small enough, a few hundred lines, the other about 10,000 lines. I also have a custom program that shows detail on a single form, if you can install it where you are (possibly I need to pull out some extraneous stuff that uses libraries) you will enjoy seeing how representation counts go up and down for the single form you specify. | |
| Dec 12, 2016 at 17:56 | comment | added | Will Jagy | @WillSawin messages out of sync. If I can figure out your email I can send you two things, the full run I did but just the record ratios, along with the much larger file giving a pretty full statement for each form. Let me try sending you some text files, begin with that. | |
| Dec 12, 2016 at 17:53 | comment | added | Will Jagy | @WillSawin the person I know who is really quick with local densities is Shimura student Jon Hanke, of the 290 theorem. He now works for a financial math place in Princeton, probably visits Bhargava and some math talks there; he does juggling on campus, there is a club. wordpress.jonhanke.com | |
| Dec 12, 2016 at 17:52 | comment | added | Will Sawin | Well let's try to guess by reading the table. We can guess that for forms where the maximum ratio is achieved for $n$ large, that in fact the ratio is an asymptotic. That means it's unlikely that there is a cusp form contribution - otherwise we would get above the asymptotic for low $n$. On the other hand, when the maximum is achieved for $n$ small, I think we can guess the reverse. | |
| Dec 12, 2016 at 17:47 | comment | added | Will Jagy | @WillSawin I don't think I remember how to calculate representation counts for a positive form. It has been a long time. I just ran these forms from Nipp's tables, up to bound 200 this time. In particular, the part about 15 sigma and 20 sigma is purely observation. | |
| Dec 12, 2016 at 12:07 | comment | added | Will Sawin | For how long do you get a simple formula (i.e. no cusp form contributions)? For how high a discriminant can you explicitly prove the bounds you are stating? I want to see how far we are from "linking up". I can now give explicit bounds that aren't too shabby, modulo the cusp form contributions. | |
| Dec 12, 2016 at 2:47 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Dec 11, 2016 at 21:21 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Dec 11, 2016 at 20:20 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Dec 11, 2016 at 19:41 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Dec 11, 2016 at 3:54 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Dec 10, 2016 at 19:06 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Dec 10, 2016 at 18:58 | history | answered | Will Jagy | CC BY-SA 3.0 |