从二元Hermite型到欧氏Bianchi群的抛物上圈
From Binary Hermitian Forms to parabolic cocycles of Euclidean Bianchi groups
摘要：
本文研究一类函数族，它以一种非常简单的方式定义为二元厄米特形式的幂和，系数在欧氏虚二次域$K$的整数环中，具有判别式$d_K$ .利用这些函数，我们构造了一个非平凡的上循环属于空间的抛物上循环的欧几里得Bianchi群。我们还证明了这些函数的平均值与$L(χ_{d_K},s)$的特殊值有关。利用这些函数的性质，我们给出了计算$L(χ_{d_K},s)$的一些特殊值的新的和计算效率高的公式。
英文摘要：
We study a family of functions defined in a very simple way as sums of powers of binary Hermitian forms with coefficients in the ring of integers of an Euclidean imaginary quadratic field $K$ with discriminant $d_K$. Using these functions we construct a nontrivial cocycle belonging to the space of parabolic cocycles on Euclidean Bianchi groups. We also show that the average value of these functions is related to the special values of $L(χ_{d_K},s)$. Using the properties of these functions we give new and computationally efficient formulas for computing some special values of $L(χ_{d_K},s)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
