Dedekind zetas和Dirichlet L-函数的广义黎曼假设的证明
Proof of generalized Riemann hypothesis for Dedekind zetas and Dirichlet L-functions
摘要：
在Hecke证明$ζ_{k}$的函数方程和[ $M_{A}$ ]（黎曼假设的代数证明）中证明黎曼假设的方法的基础上，给出了代数数域$k$ -的zeta函数$ζ_{k}$的广义黎曼假设（简称gRH）的一个简短证明. Dirichlet L-函数的广义黎曼假设是$ζ_{k}$的（gRH）和连接Dedekind zeta与L-函数的适当乘积公式的直接结果。
英文摘要：
A short proof of the generalized Riemann hypothesis (gRH in short) for zeta functions $ζ_{k}$ of algebraic number fields $k$ - based on the Hecke's proof of the functional equation for $ζ_{k}$ and the method of the proof of the Riemann hypothesis derived in [$M_{A}$] (algebraic proof of the Riemann hypothesis) is given. The generalized Riemann hypothesis for Dirichlet L-functions is an immediately consequence of (gRH) for $ζ_{k}$ and suitable product formula which connects the Dedekind zetas with L-functions.
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。
