论文标题
一种通用下限，用于一定的二次二次积分。
A universal lower bound for certain quadratic integrals of automorphic L-functions
论文作者
论文摘要
我们获得了均匀的下限，对于与GL（m，a）相关的所有自动形态L功能l（s）l（s），其中a表示垂直线上的积分（re（re（re（s）= 1/2））绝对值平方的f ligonals q的adeles；当S_0是关键线上L功能的零时，也是L（s）/（S-S_0）的。对于临界带中不同横坐标的垂直积分，也以小度m获得了几种变体。对于证明融合所需的估计值，我们被概括为Friedlander-iwaniec的结果（Can。J.Math。57,2005）。我们获得了关于L系列收敛性如果活的新结果。最后，当S_0倾向于无限时，特别是对于Riemann Zeta函数时，对二次积分的行为提出了一个问题。
We obtain uniform lower bounds, true for all automorphic L-functions L(s) associated to cuspidal representations of GL(m,A) where A denotes the adeles of the rationals Q, of the integral on the vertical line (Re(s)=1/2) of the absolute value squared of L(s)/s; and also of L(s)/(s-s_0) when s_0 is a zero of the L-function on the critical line. Several variants are also obtained in small degrees m, for the vertical integrals at different abscissas in the critical strip. For the estimates required to prove convergence, we are led to generalise a result of Friedlander-Iwaniec (Can. J. Math. 57,2005). We obtain new results on the abscissa of convergence of the L-series. Finally, a problem is posed about the behaviour of the quadratic integral when s_0 tends to infinity, in particular for the Riemann zeta function.
