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math.NT2011★ 2 cited
On the sup-norm of Maass cusp forms of large level. III
Gergely Harcos, Nicolas Templier
Let be a Hecke--Maass cuspidal newform of square-free level and Laplacian eigenvalue . It is shown that $\pnorm{f}_\infty \ll_{λ,ε} N^{-1/6}+ε} \pnorm{f}_2$ for any $ε>0…
math.NT2011
Non-split Sums of Coefficients of GL(2)-Automorphic Forms
Nicolas Templier, Jacob Tsimerman
Given a cuspidal automorphic form on $\GL_2$, we study smoothed sums of the form . The error term we get is sharp in that it is…