Hi QForms folks,<\/p>\n
This week, Lee Troupe will be giving a talk titled “Towards a Function Field Cochrane-Mitchell Theorem.” The abstract is below — hope you see you all there!<\/p>\n
-Danny<\/p>\n
Abstract: In the initial discussion of Legendre’s Theorem, it was made clear that may be viewed as the n = 3, K = Q case of the celebrated Hasse-Minkowski Theorem.\u00a0 In general, it is a natural (and wide open!) problem to find other cases of Hasse-Minkowski which can be proved by GoN methods.\u00a0 One advantage of the GoN approach is that there is also the prospect for an explicit upper bound on the size of an isotropic vector.\u00a0 (This is also largely an open problem: when explicit bounds are known, they are generally known not to be\u00a0sharp<\/em>\u00a0in any reasonable sense.)<\/p>\n In this talk we pursue the case n = 3, K = F_q(t), where q is an odd prime power.\u00a0 Both linear forms and Hermite constants have proven analogues in this context.\u00a0 Perhaps surprisingly, linear forms methods seem more auspicious; in particular, absent a meaningful notion of “majorization” in this context, an approach via Hermite constants doesn’t yield explicit bounds.\u00a0 We will present a linear forms theorem due to L. Tornheim and try to apply it to prove a Cochrane-Mitchell type result.\u00a0 This is work (jointly with Pete L. Clark) in progress: as of this writing, it seems that we can prove the result when deg(a), deg(b), deg(c) are neither all even nor all odd.\u00a0 Help from the audience will be warmly appreciated.<\/p>\n","protected":false},"excerpt":{"rendered":" Hi QForms folks, This week, Lee Troupe will be giving a talk titled “Towards a Function Field Cochrane-Mitchell Theorem.” The abstract is below — hope you see you all there! -Danny Abstract: In the initial discussion of Legendre’s Theorem, it … Continue reading