JournalsjemsVol. 19, No. 11pp. 3549–3573

On sup-norms of cusp forms of powerful level

  • Abhishek Saha

    University of Bristol, UK
On sup-norms of cusp forms of powerful level cover
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Abstract

Let ff be an L2L^2-normalized Hecke–Maass cuspidal newform of level NN and Laplace eigenvalue λ\lambda. It is shown that fλ,ϵN1/12+ϵ\|f\|_\infty \ll_{\lambda, \epsilon} N^{-1/12 + \epsilon} for any ϵ>0\epsilon > 0. The exponent is further improved in the case when NN is not divisible by "small squares". Our work extends and generalizes previously known results in the special case of NN squarefree.

Cite this article

Abhishek Saha, On sup-norms of cusp forms of powerful level. J. Eur. Math. Soc. 19 (2017), no. 11, pp. 3549–3573

DOI 10.4171/JEMS/746