dc.contributor.author | Saha, A | en_US |
dc.date.accessioned | 2017-08-23T09:39:12Z | |
dc.date.available | 2016-12-16 | en_US |
dc.date.issued | 2017-07-12 | en_US |
dc.date.submitted | 2017-08-15T15:03:14.799Z | |
dc.identifier.issn | 1937-0652 | en_US |
dc.identifier.uri | http://qmro.qmul.ac.uk/xmlui/handle/123456789/25407 | |
dc.description | Postprint version; to appear in Algebra and Number Theory | en_US |
dc.description | Postprint version; to appear in Algebra and Number Theory | en_US |
dc.description | Postprint version; to appear in Algebra and Number Theory | en_US |
dc.description.abstract | Let $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$, character $\chi$ and Laplace eigenvalue $\lambda$. Let $N_1$ denote the smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer such that $N_0^2 |N$. Let $M$ denote the conductor of $\chi$ and define $M_1= M/\gcd(M,N_1)$. In this paper, we prove the bound $|f|_\infty$ $\ll_{\epsilon}$ $N_0^{1/6 + \epsilon} N_1^{1/3+\epsilon} M_1^{1/2} \lambda^{5/24+\epsilon}$, which generalizes and strengthens previously known upper bounds for $|f|_\infty$. This is the first time a hybrid bound (i.e., involving both $N$ and $\lambda$) has been established for $|f|_\infty$ in the case of non-squarefree $N$. The only previously known bound in the non-squarefree case was in the N-aspect; it had been shown by the author that $|f|_\infty \ll_{\lambda, \epsilon} N^{5/12+\epsilon}$ provided $M=1$. The present result significantly improves the exponent of $N$ in the above case. If $N$ is a squarefree integer, our bound reduces to $|f|_\infty \ll_\epsilon N^{1/3 + \epsilon}\lambda^{5/24 + \epsilon}$, which was previously proved by Templier. The key new feature of the present work is a systematic use of p-adic representation theoretic techniques and in particular a detailed study of Whittaker newforms and matrix coefficients for $GL_2(F)$ where $F$ is a local field. | en_US |
dc.publisher | Mathematical Sciences Publishers | en_US |
dc.relation.ispartof | Algebra and Number Theory | en_US |
dc.rights | This is a pre-copyedited, author-produced version of an article accepted for publication in Mathematical Sciences Publishers following peer review. The version of record is available http://msp.org/ant/2017/11-5/p01.xhtml | |
dc.subject | math.NT | en_US |
dc.subject | math.NT | en_US |
dc.subject | math.RT | en_US |
dc.subject | math.SP | en_US |
dc.title | Hybrid sup-norm bounds for Maass newforms of powerful level | en_US |
dc.type | Article | |
dc.rights.holder | © 2017 Mathematical Sciences Publishers | |
dc.identifier.doi | 10.2140/ant.2017.11.1009 | en_US |
pubs.author-url | http://arxiv.org/abs/1509.07489v4 | en_US |
pubs.notes | Not known | en_US |
pubs.publication-status | Published | en_US |
dcterms.dateAccepted | 2016-12-16 | en_US |