论文标题
光谱方面subconvex bends $ {\ rm u} _ {n+1} \ times {\ rm u} _ {n} $
Spectral aspect subconvex bounds for ${\rm U}_{n+1} \times {\rm U}_{n}$
论文作者
论文摘要
令$（π，σ）$穿越一对单一gan-gross-gross-prasad Pair $（{\ rm u} _ {n+1}，{\ rm U} _n）$的单位gan-gross-prasad pair $（{\ rm u} _ {\ rm u} _ {\ rm u} _ {\ rm u} _n）$的序列均与$ {\ rm um u} $ anis anisoc。我们假设在某个杰出的阿基米德地方，两人远离导体掉落的位点，而在其他每个地方，这对夫妇都界定了分支并满足某些地方条件（尤其是脾气暴躁）。我们证明，子convex绑定\ [l（π\ timesσ，1/2）\ ll c（π\ timesσ）^{1/4-δ} \]对于任何固定\ [Δ<\ frac {1} {8 n^5 n n^5 + 28 n^4^4^42 n^42 n^42 N^3^3 + 36 n^ + 14 n}的任何固定\ [Δ<\ frac {1} \]除其他成分外，该证明还采用了用A. venkatesh开发的谎言组表示的微局部演算的改进，并观察到了Marshall S. Marshall关于相对痕量公式的几何侧。
Let $(π,σ)$ traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan--Gross--Prasad pair $({\rm U}_{n+1},{\rm U}_n)$ over a number field, with ${\rm U}_n$ anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local conditions (in particular, temperedness). We prove that the subconvex bound \[ L(π\times σ,1/2) \ll C(π\times σ)^{1/4 - δ} \] holds for any fixed \[ δ< \frac{1}{8 n^5 + 28 n^4 + 42 n^3 + 36 n^2 + 14 n}. \] Among other ingredients, the proof employs a refinement of the microlocal calculus for Lie group representations developed with A. Venkatesh and an observation of S. Marshall concerning the geometric side of the relative trace formula.
