DC Field | Value | Language |
---|---|---|
dc.contributor.author | Jung, Junehyuk | ko |
dc.date.accessioned | 2016-11-29T05:04:45Z | - |
dc.date.available | 2016-11-29T05:04:45Z | - |
dc.date.created | 2016-11-08 | - |
dc.date.created | 2016-11-08 | - |
dc.date.issued | 2016-12 | - |
dc.identifier.citation | COMMUNICATIONS IN MATHEMATICAL PHYSICS, v.348, no.2, pp.603 - 653 | - |
dc.identifier.issn | 0010-3616 | - |
dc.identifier.uri | http://hdl.handle.net/10203/214091 | - |
dc.description.abstract | We prove a quantitative statement of the quantum ergodicity for Hecke-Maass cusp forms on the modular surface. As an application of our result, along a density 1 subsequence of even Hecke-Maass cusp forms, we obtain a sharp lower bound for the L2-norm of the restriction to a fixed compact geodesic segment of eta = {iy : y > 0} subset of H. We also obtain an upper bound of O-epsilon (t(phi)(3/8+epsilon)) for the L-infinity norm along a density 1 subsequence of Hecke-Maass cusp forms; for such forms, this is an improvement over the upper bound of O-epsilon (t(phi)(5/12+epsilon)) given by Iwaniec and Sarnak. In a recent work of Ghosh, Reznikov, and Sarnak, the authors proved for all even Hecke-Maass forms that the number of nodal domains, which intersect a geodesic segment of eta, grows faster than t(phi)(1/12-epsilon) for any epsilon > 0, under the assumption that the Lindelof Hypothesis is true and that the geodesic segment is long enough. Upon removing a density zero subset of even Hecke-Maass forms, we prove without making any assumptions that the number of nodal domains grows faster than t(phi)(1/8+epsilon) for any epsilon > 0 | - |
dc.language | English | - |
dc.publisher | SPRINGER | - |
dc.subject | UNIQUE ERGODICITY | - |
dc.subject | BOUNDARY-VALUES | - |
dc.subject | EIGENFUNCTIONS | - |
dc.subject | EQUIDISTRIBUTION | - |
dc.subject | RESTRICTION | - |
dc.subject | EIGENFORMS | - |
dc.subject | SURFACES | - |
dc.subject | SERIES | - |
dc.subject | NUMBER | - |
dc.subject | NORMS | - |
dc.title | Quantitative Quantum Ergodicity and the Nodal Domains of Hecke-Maass Cusp Forms | - |
dc.type | Article | - |
dc.identifier.wosid | 000385166500008 | - |
dc.identifier.scopusid | 2-s2.0-84977178423 | - |
dc.type.rims | ART | - |
dc.citation.volume | 348 | - |
dc.citation.issue | 2 | - |
dc.citation.beginningpage | 603 | - |
dc.citation.endingpage | 653 | - |
dc.citation.publicationname | COMMUNICATIONS IN MATHEMATICAL PHYSICS | - |
dc.identifier.doi | 10.1007/s00220-016-2694-8 | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | UNIQUE ERGODICITY | - |
dc.subject.keywordPlus | BOUNDARY-VALUES | - |
dc.subject.keywordPlus | EIGENFUNCTIONS | - |
dc.subject.keywordPlus | EQUIDISTRIBUTION | - |
dc.subject.keywordPlus | RESTRICTION | - |
dc.subject.keywordPlus | EIGENFORMS | - |
dc.subject.keywordPlus | SURFACES | - |
dc.subject.keywordPlus | SERIES | - |
dc.subject.keywordPlus | NUMBER | - |
dc.subject.keywordPlus | NORMS | - |
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