Timeline for Which quaternary quadratic form represents $n$ the greatest number of times?

11 events

when toggle format	what		by	license	comment
Dec 10, 2016 at 18:58	answer	added	Will Jagy		timeline score: 4
Dec 8, 2016 at 22:05	answer	added	Will Sawin		timeline score: 12
Dec 8, 2016 at 21:33	comment	added	GH from MO		I added Valentin Blomer's remarks under my post, which show that in fact we have $r_Q(n)\ll\sigma(n)$ with an absolute implied constant.
Dec 8, 2016 at 14:36	vote	accept	Jeremy Rouse
Dec 7, 2016 at 22:36	history	edited	GH from MO		edited tags
Dec 7, 2016 at 22:26	answer	added	GH from MO		timeline score: 20
Dec 7, 2016 at 18:25	history	edited	Jeremy Rouse	CC BY-SA 3.0	added 153 characters in body
Dec 7, 2016 at 18:24	answer	added	joro		timeline score: 3
Dec 7, 2016 at 16:45	comment	added	Will Jagy		forms with a square factor in the discriminant that are represented by a form of lower discriminant cannot be the best. Similar if a form is anisotropic at some prime, although you may then consider $n$ not divisible by that prime. Easy enough to do a competition for the first few forms in Nipp's tables, and target numbers up to a modest bound. Need to see whether I ever wrote a function to count representations for quaternaries.
Dec 7, 2016 at 14:04	comment	added	Kimball		One possibility for a partial result: restrict to $Q$ being a norm form from a quaternion algebra, and use bounds for the number of elements of norm $n$ in a maximal order. (See Conway-Smith for the case of Hamilton's quaternions over $\mathbb Q$.)
Dec 6, 2016 at 22:09	history	asked	Jeremy Rouse	CC BY-SA 3.0