论文标题
关于J-Bessel功能的积分及其在Mahler量度的应用（用J.S. Friedman的附录*）
On an integral of J-Bessel functions and its application to Mahler measure (with an appendix by J.S. Friedman*)
论文作者
论文摘要
在最近的论文中，Cogdell，Jorgenson和Smajlović的团队为对数的Mahler量度制定了无限的串联表示，其中一个复杂的线性形式，具有4个或更多变量。我们通过与积分与积分进行界定，涉及随机步行概率密度$ a \ displayStyle \ int_0^\ int_0^\ infty tj_0（at）\ displayStyle \ prod_ {m = 0}^2 j_0（r_m t）dt $ j_0 $ j_0 $是$ j_5 {$ r_m $}是正实数。为了促进我们的证据，我们在已知的分歧点上对整体的渐近行为进行了替代描述。作为适应数值实验的计算辅助工具，附录中介绍了一种计算这些系列的算法。
In a recent paper the team of Cogdell, Jorgenson and Smajlović develop infinite series representations for the logarithmic Mahler measure of a complex linear form, with 4 or more variables. We establish the case of 3 variables, by bounding an integral with integrand involving the random walk probability density $a\displaystyle\int_0^\infty tJ_0(at) \displaystyle\prod_{m=0}^2 J_0(r_m t)dt$, where $J_0$ is the order zero Bessel function of the first kind, and $a$ and {$r_m$} are positive real numbers. To facilitate our proof we develop an alternative description of the integral's asymptotic behavior at its known points of divergence. As a computational aid to accommodate numerical experiments, an algorithm to calculate these series is presented in the Appendix.
