论文标题
中央值的Dirichlet $ L $ functions的第四刻
The fourth moment of Dirichlet $L$-functions at the central value
论文作者
论文摘要
Dirichlet $ L $ functions的第四刻的渐近公式是由J. B. Conrey，D。W. Farmer，J。P。Keating，M。O。Rubinstein和N. C. Snaith和N. C. Snaith和N. C. Snaith和Prime Moduli案的猜想预测。这项工作依赖于特殊的除数函数的研究，称为$ \ Mathcal {d} _q $ - 功能，该功能在推论主要术语中起着关键作用。另一个关键要素是在误差术语估计中应用的Kloosterman总和中的新界限应用。
The asymptotic formula of the fourth moment of Dirichlet $L$-functions at the central value was predicted in a conjecture by J. B. Conrey, D. W. Farmer, J. P. Keating, M. O. Rubinstein, and N. C. Snaith, and the prime moduli case was proved by M. P. Young in 2011. This work establishes this asymptotic formula for general moduli. The work relies on the study of a special divisor sum function, called $\mathcal{D}_q$-function, which plays a key role in deducing the main terms. Another key ingredient is an application of new bounds for double sums in Kloosterman sums, applied in the estimate of the error terms.
