Double first moment for L(1/2, Sym(2)f x g) by applying Petersson's formula twice
Double first moment for L(1/2, Sym(2)f x g) by applying Petersson's formula twice
复制标题
通过应用 Petersson 公式两次，将 L(1/2, Sym(2)f x g) 的一阶矩加倍
DOI：
10.1016/j.jnt.2019.01.014
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发表时间：
2019
影响因子：
0.7
通讯作者：
Ye Yangbo
中科院分区：
文献类型：
--
作者：
Sun Haiwei;Ye Yangbo
对于S L （2， Z）的权值为k1的全纯顶点形式f和权值为k2的g，证明了L （1 2, Sym 2 fx g）对f和g的和的界。由于已知这些中心值是非负的，因此f和g的平均值的Lindelöf假设如下。因此，对于任意权值k1以某种方式趋近于∞的f，证明了g上中心值的和的界。在两个权重方面，对于所有f和除了相对少数例外g之外的所有例外g，也建立了单个中心值的子凸界。作为一个应用，也建立了三重积L函数L （s, fx fx g）的子凸界。这些非异常g的次凸边界允许f移动并超过所有已知边界和weyl型边界的强度。
For holomorphic cusp forms f of weight k 1 and g of weight k 2 for S L (2, Z), bounds are proved for sums of L (1 2, Sym 2 f× g) over both f and g. Since these central values are known to be non-negative, the Lindelöf Hypothesis on average for both f and g follows. As a consequence, bounds for sums of the central values over g are proved for any f with its weight k 1 tending to∞ in certain ways. Subconvexity bounds for individual central values are also established in the two weight aspects for all f and all but a relatively small number of exceptional g. As an application, subconvexity bounds for the triple product L-function L (s, f× f× g) are also established. These subconvexity bounds for non-exceptional g's allow f to move and exceed the strength of all known bounds and the Weyl-type bound.