Skip to content
Accessible Unlicensed Requires Authentication Published by De Gruyter July 5, 2015

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

Soumya Das and Jyoti Sengupta
From the journal Forum Mathematicum

Abstract

We prove a sub-convex estimate for the sup-norm of L2-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 L2 norm of an eigenfunction f is one,

fεk12-133+ε

for any ε>0 and for all k sufficiently large.

Funding source: DST-INSPIRE

Award Identifier / Grant number: IFA 12-MA-13

It is a great pleasure for the authors to thank Professor Peter Sarnak for his thoughtful comments on the paper. We also thank the School of Mathematics TIFR, Mumbai and the Department of Mathematics, IISc., Bangalore, where parts of this work was carried out, for providing excellent working atmosphere. The authors are grateful to the anonymous referee for a careful reading of the paper and for many helpful suggestions that improved the presentation.

Received: 2013-1-8
Revised: 2013-4-23
Published Online: 2015-7-5
Published in Print: 2015-7-1

© 2015 by De Gruyter