dc.contributor.author | Nelson, PD | en_US |
dc.contributor.author | Pitale, A | en_US |
dc.contributor.author | Saha, A | en_US |
dc.date.accessioned | 2017-08-23T09:43:25Z | |
dc.date.available | 2013-08-06 | en_US |
dc.date.issued | 2014-01-01 | en_US |
dc.date.submitted | 2017-08-15T14:54:09.470Z | |
dc.identifier.uri | http://qmro.qmul.ac.uk/xmlui/handle/123456789/25408 | |
dc.description | 43 pages; various minor corrections (many thanks to the referee) and improvements in clarity and exposition. To appear in JAMS | en_US |
dc.description | 43 pages; various minor corrections (many thanks to the referee) and improvements in clarity and exposition. To appear in JAMS | en_US |
dc.description.abstract | Let f be a classical holomorphic newform of level q and even weight k. We show that the pushforward to the full level modular curve of the mass of f equidistributes as qk -> infinity. This generalizes known results in the case that q is squarefree. We obtain a power savings in the rate of equidistribution as q becomes sufficiently "powerful" (far away from being squarefree), and in particular in the "depth aspect" as q traverses the powers of a fixed prime. We compare the difficulty of such equidistribution problems to that of corresponding subconvexity problems by deriving explicit extensions of Watson's formula to certain triple product integrals involving forms of non-squarefree level. By a theorem of Ichino and a lemma of Michel--Venkatesh, this amounts to a detailed study of Rankin--Selberg integrals int|f|^2 E attached to newforms f of arbitrary level and Eisenstein series E of full level. We find that the local factors of such integrals participate in many amusing analogies with global L-functions. For instance, we observe that the mass equidistribution conjecture with a power savings in the depth aspect is equivalent to the union of a global subconvexity bound and what we call a "local subconvexity bound"; a consequence of our local calculations is what we call a "local Lindelof hypothesis". | en_US |
dc.publisher | American Mathematical Society | en_US |
dc.relation.ispartof | Journal of the American Mathematical Society | en_US |
dc.rights | This is a pre-copyedited, author-produced version of an article accepted for publication in American Mathematical Society following peer review. The version of record is available http://www.ams.org/journals/jams/2014-27-01/S0894-0347-2013-00779-1/ | |
dc.subject | math.NT | en_US |
dc.subject | math.NT | en_US |
dc.subject | math.DS | en_US |
dc.subject | 11F11 (Primary) 11F70, 22E50, 58J51 (Secondary) | en_US |
dc.title | Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels | en_US |
dc.type | Article | |
dc.rights.holder | © Copyright 2013 American Mathematical Society | |
dc.identifier.doi | 10.1090/S0894-0347-2013-00779-1 | en_US |
pubs.notes | Not known | en_US |
pubs.publication-status | Published | en_US |
dcterms.dateAccepted | 2013-08-06 | en_US |