论文标题
关于对称功率l功能在级别方面的对数的价值分布
On the value-distribution of the logarithms of symmetric power L-functions in the level aspect
论文作者
论文摘要
我们考虑与重量和质量功率水平的新形式相关的对称功率L功能的对数的价值分布。在对称平方案例中，在某些合理的分析条件下，我们证明这些值在级别方面的某些平均值，涉及连续有界或Riemann可集成的测试功能，可以写成涉及与SATO-TATE度量相关的密度函数（“ M功能”）的积分。此外，即使在一般对称功率L功能的情况下，当某些特殊类型的测试功能时，我们也会显示出相同类型的公式。我们看到，存在密度函数的一种奇偶校验现象。
We consider the value distribution of logarithms of symmetric power L-functions associated with newforms of even weight and prime power level. In the symmetric square case, under certain plausible analytical conditions, we prove that certain averages of those values in the level aspect, involving continuous bounded or Riemann integrable test functions, can be written as integrals involving a density function (the "M-function") which is related with the Sato-Tate measure. Moreover, even in the case of general symmetric power L-functions, we show the same type of formula when for some special type of test functions. We see that a kind of parity phenomenon of the density function exists.
