Geodesic
On sup-norms of cusp forms of powerful level
Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3549-3573.

Voir la notice de l'article provenant de la source EMS Press

Let f be an L2-normalized Hecke–Maass cuspidal newform of level N and Laplace eigenvalue λ. It is shown that ∥f∥∞​≪λ,ε​N−1/12+ε for any ε>0. The exponent is further improved in the case when N is not divisible by "small squares". Our work extends and generalizes previously known results in the special case of N squarefree.
DOI : 10.4171/jems/746
Classification : 11-XX, 00-XX
Keywords: Maass form, sup-norm, Fourier coefficients, amplification 
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     author = {Abhishek Saha},
     title = {On sup-norms of cusp forms of powerful level},
     journal = {Journal of the European Mathematical Society},
     pages = {3549--3573},
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     year = {2017},
     doi = {10.4171/jems/746},
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Abhishek Saha. On sup-norms of cusp forms of powerful level. Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3549-3573. doi : 10.4171/jems/746. http://geodesic.mathdoc.fr/articles/10.4171/jems/746/

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