## Duke Mathematical Journal

### Distribution of mass of holomorphic cusp forms

#### Abstract

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

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

Dates
Revised: 22 February 2013
First available in Project Euclid: 6 November 2013

https://projecteuclid.org/euclid.dmj/1383760700

Digital Object Identifier
doi:10.1215/00127094-2380967

Mathematical Reviews number (MathSciNet)
MR3127809

Zentralblatt MATH identifier
1312.11028

#### Citation

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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