Geodesic
On sup-norms of cusp forms of powerful level
Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3549-3573 Cet article a éte moissonné depuis la source EMS Press

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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 
@article{JEMS_2017_19_11_a7,
     author = {Abhishek Saha},
     title = {On sup-norms of cusp forms of powerful level},
     journal = {Journal of the European Mathematical Society},
     pages = {3549--3573},
     year = {2017},
     volume = {19},
     number = {11},
     doi = {10.4171/jems/746},
     url = {http://geodesic.mathdoc.fr/articles/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

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