Weak subconvexity without a Ramanujan hypothesis
Weak subconvexity without a Ramanujan hypothesis
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DOI：
10.1215/00127094-2018-0065
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发表时间：
2018-04
影响因子：
2.5
通讯作者：
K. Soundararajan;Jesse Thorner
中科院分区：
文献类型：
--
作者：
K. Soundararajan;Jesse Thorner
我们描述了一种新的方法来获得弱次凸界的$L$-函数的Dirichlet系数的大小的温和的假设。我们验证这些假设的所有自守$L$-功能和（轻度限制）的Rankin-Selberg $L$-功能连接到两个自守表示。证明依赖于Rankin-Selberg $L$-函数的一个新的无条件无对数零密度估计。
We describe a new method to obtain weak subconvexity bounds for $L$-functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all automorphic $L$-functions and (with mild restrictions) the Rankin-Selberg $L$-functions attached to two automorphic representations. The proof relies on a new unconditional log-free zero density estimate for Rankin-Selberg $L$-functions.