JournalsjemsVol. 15, No. 5pp. 1825–1852

On the 4-norm of an automorphic form

  • Valentin Blomer

    Georg-August-Universität Göttingen, Germany
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Abstract

We prove the optimal upper bound ff44qε\sum_f \| f \|_4^4 \ll q^{\varepsilon} where ff runs over an orthonormal basis of Maa{\ss} cusp forms of prime level qq and bounded spectral parameter.

Cite this article

Valentin Blomer, On the 4-norm of an automorphic form. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1825–1852

DOI 10.4171/JEMS/405