SelectedPapers.net is a free, open-source project aimed at improving the way people find, read, and share academic papers. By looking at the intersection of people and ideas, we can help deliver content specifically tuned to your interests. But we're just getting started, and we can use your help. This is an initial, alpha release of SelectedPapers.net. Please give us your feedback: either general comments or specific new bug reports or feature suggestions.
Try out our new People, Topics and Comments search options above! We have a new discussion forum. Also please subscribe for news about spnet. If your Google+ post is failing to appear here, click here for a quick solution.
Give it a try by signing in below, or learn more about how it works:
+Mark Lewko As Ben says, without the explicit dependence of constants on k one probably doesn't immediately get new bounds on zeta; for instance even the deep results of Wooley in recent years have not (to my knowledge) budged the classical Vinogradov-Korobov zerofree region on zeta, which is proven using the classical Vinogradov mean value theorem. But perhaps some variant of the methods can say something new. Recently for instance Bourgain used the decoupling theorem to slightly improve the upper bound on zeta on the critical line (making a little bit of progress towards the Lindelof hypothesis). Naively one could perhaps hope to somehow combine the decoupling methods with the efficient congruencing methods to prove some super-theorem that could have further applications, though currently the methods look very incompatible (the latter relies very much on the arithmetic structure, while the former heavily relies on generalising to the non-arithmetic setting for induction purposes).