论文标题
hecke的立方时刻 - 马斯尖端形式和$ l $ functions的时刻
The cubic moment of Hecke--Maass cusp forms and moments of $L$-functions
论文作者
论文摘要
在本文中，我们证明了光滑的立方矩消失了hecke-maass尖端形式，这给出了随机波的新案例。实际上，我们可以证明平滑的立方矩的多项式衰减，而对于普通的衰减率平滑（即que），对于一般的hecke-maass cusp形式而言，衰减的速率无条件无条件。对中央$ l $价值的时刻的各种估计的证明基础。我们证明，$ \ rm gl（3）\ times gl（2）$ $ $ $ l $ functions的第一瞬间的平均限制在亚凸强度长度的短期间隔，并且在$ \ rm gl（2）$的混合力矩和Triple Product $ l $ l $ l $ lunctions的混合力矩上，凸强度上限。特别是，我们证明了某些$ \ rm gl（3）\ times gl（2）$ $ $ l $ functions的新subconvexity范围。
In this paper, we prove the smooth cubic moments vanish for the Hecke--Maass cusp forms, which gives a new case of the random wave conjecture. In fact, we can prove a polynomial decay for the smooth cubic moments, while for the smooth second moment (i.e. QUE) no rate of decay is known unconditionally for general Hecke--Maass cusp forms. The proof bases on various estimates of moments of central $L$-values. We prove the Lindelöf on average bound for the first moment of $\rm GL(3)\times GL(2)$ $L$-functions in short intervals of the subconvexity strength length, and the convexity strength upper bound for the mixed moment of $\rm GL(2)$ and the triple product $L$-functions. In particular, we prove new subconvexity bounds of certain $\rm GL(3)\times GL(2)$ $L$-functions.
