论文标题
theta功能，特征形式的第四矩和Sup-Norm问题II
Theta functions, fourth moments of eigenforms, and the sup-norm problem II
论文作者
论文摘要
对于$ l^2 $均匀的全态性holomorphic newform $ f $ f $ f $ k $ $ k $在卷$ v $的双曲表面上附加到无定义的四季度代数，超过$ \ mathbb {q} $ \ [ \ | \ im（\ cdot）^{\ frac {k} {2}} f \ | _ {\ infty} \ll_ε（k v）^{\ frac {1} {4} {4}+ε} \]绝对隐含常数。对于cuspidalmaaß新形式$φ$ eigenvalue $λ$在这样的表面上，我们证明 \ [ \ |φ\ | _ {\ infty} \ ll_ {λ，ε} v^{\ frac {1} {4} {4}+ε}。 \] 我们在确定的四元组代数的环境中建立了类似的估计。
For an $L^2$-normalized holomorphic newform $f$ of weight $k$ on a hyperbolic surface of volume $V$ attached to an Eichler order of squarefree level in an indefinite quaternion algebra over $\mathbb{Q}$, we prove the sup-norm estimate \[ \| \Im(\cdot)^{\frac{k}{2}} f \|_{\infty} \ll_ε (k V)^{\frac{1}{4}+ε} \] with absolute implied constant. For a cuspidal Maaß newform $φ$ of eigenvalue $λ$ on such a surface, we prove that \[ \|φ\|_{\infty} \ll_{λ,ε} V^{\frac{1}{4}+ε}. \] We establish analogous estimates in the setting of definite quaternion algebras.
