Duke Mathematical Journal

Distribution of mass of holomorphic cusp forms

Valentin Blomer, Rizwanur Khan, and Matthew Young

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We prove an upper bound for the L 4 -norm and for the L 2 -norm restricted to the vertical geodesic of a holomorphic Hecke cusp form f of large weight k . The method is based on Watson’s formula and estimating a mean value of certain L -functions of degree 6. Further applications to restriction problems of Siegel modular forms and subconvexity bounds of degree 8 L -functions are given.

Article information

Duke Math. J., Volume 162, Number 14 (2013), 2609-2644.

Received: 12 March 2012
Revised: 22 February 2013
First available in Project Euclid: 6 November 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations


Blomer, Valentin; Khan, Rizwanur; Young, Matthew. Distribution of mass of holomorphic cusp forms. Duke Math. J. 162 (2013), no. 14, 2609--2644. doi:10.1215/00127094-2380967. https://projecteuclid.org/euclid.dmj/1383760700

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