论文标题
theta功能，特征形式的第四瞬间和Sup-Norm问题I
Theta functions, fourth moments of eigenforms, and the sup-norm problem I
论文作者
论文摘要
我们在与艾希勒订单相关的算术双曲表面上的第四矩重量范围内给出了尖锐的点界。因此，我们加强了Xia的结果，并将其扩展到共同型晶格。我们通过在$ \ Mathbf {g} \ times \ times \ Mathbf {g} \ Times \ Times \ MathBf {Sl} _ {2} $上构建Holomorthic Theta内核来实现这一第四刻。 $ \ mathbb {q} $，基于Bergman内核，并考虑其$ l^2 $ -norm在Weil变量中。构建的theta内核进一步引起了新的基本theta系列，用于签名$（2,2）$的整体二次形式。
We give sharp point-wise bounds in the weight-aspect on fourth moments of modular forms on arithmetic hyperbolic surfaces associated to Eichler orders. Therefore we strengthen a result of Xia and extend it to co-compact lattices. We realize this fourth moment by constructing a holomorphic theta kernel on $\mathbf{G} \times \mathbf{G} \times \mathbf{SL}_{2}$, for $\mathbf{G}$ an indefinite inner-form of $\mathbf{SL}_2$ over $\mathbb{Q}$, based on the Bergman kernel, and considering its $L^2$-norm in the Weil variable. The constructed theta kernel further gives rise to new elementary theta series for integral quadratic forms of signature $(2,2)$.
