除数矩阵、Dirichlet 级数与 SL(2,Z)
数论
2020-01-30 v6 群论
摘要
构造了 SL(2,Z) 通过整数矩阵作用于解析普通 Dirichlet 级数空间的一个表示，其中标准单幂元的作用表现为乘以 Riemann zeta 函数。随后证明了 zeta 函数轨道中的 Dirichlet 级数通过代数方程与之相关联。
引用
@article{arxiv.0712.0837,
title = {The Divisor Matrix, Dirichlet Series and SL(2,Z)},
author = {Peter Sin and John G. Thompson},
journal= {arXiv preprint arXiv:0712.0837},
year = {2020}
}
备注
29 pages. The current version V4 is the combination of two papers, previously called parts I and II, with the same title. Part II had been posted as arXiv:0803.1121v5. Some additional remarks added in section 10. V6. Minor errors corrected