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L-infinity norms of holomorphic modular forms in the case of compact quotient

Das, Soumya and Sengupta, Jyoti (2015) L-infinity norms of holomorphic modular forms in the case of compact quotient. In: FORUM MATHEMATICUM, 27 (4). pp. 1987-2001.

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Official URL: http://dx.doi.org/10.1515/forum-2013-6004

Abstract

We prove a sub-convex estimate for the sup-norm of L-2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over Q. More precisely we show that when the L-2 norm of an eigenfunction f is one, parallel to f parallel to(infinity) <<(epsilon) k(1/2-1/33+epsilon) for any epsilon > 0 and for all k sufficiently large.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the WALTER DE GRUYTER GMBH, GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY
Keywords: Sup-norm; sub-convexity bound; compact quotient
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 26 Aug 2015 06:38
Last Modified: 26 Aug 2015 06:38
URI: http://eprints.iisc.ac.in/id/eprint/52249

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