The mean value of L(12,χ) in the hyperelliptic ensemble
The mean value of L(12,χ) in the hyperelliptic ensemble
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DOI：
10.1016/j.jnt.2012.05.017
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发表时间：
2012-08
影响因子：
0.7
通讯作者：
J. Andrade;J. Keating
中科院分区：
文献类型：
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作者：
J. Andrade;J. Keating
我们得到了有理函数域上二次Dirichlet L-函数在中心点S=12的一阶矩的渐近公式。具体地说，我们计算了L(12，χ)对固定有限域上亏格为g的超椭圆曲线系综的期望值g→∞。我们的方法依赖于对这类L函数使用近似函数方程的类比。本文的结果是Jutila以前在数域环境下得到的函数场的类似结果，与最近由随机矩阵理论激励的L函数的矩的一般猜想是一致的。
We obtain an asymptotic formula for the first moment of quadratic Dirichlet L-functions over the rational function field at the central point s=12. Specifically, we compute the expected value of L(12,χ) for an ensemble of hyperelliptic curves of genus g over a fixed finite field as g→∞. Our approach relies on the use of the analogue of the approximate functional equation for such L-functions. The results presented here are the function field analogues of those obtained previously by Jutila in the number-field setting and are consistent with recent general conjectures for the moments of L-functions motivated by Random Matrix Theory.