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Ratios of Artin L-functions
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-08-26 , DOI: 10.1016/j.jnt.2021.07.007
Leonhard Hochfilzer 1 , Thomas Oliver 2
Affiliation  

We study the cancellation of zeros between the Riemann zeta function and certain Artin L-functions. To do so, we develop a converse theorem for Maass forms of Laplace eigenvalue 1/4 in which the twisted L-functions are not assumed to be entire. We do not require the conjectural automorphy of Artin L-functions, only their established meromorphic continuation and functional equation.



中文翻译:

Artin L-函数的比率

我们研究了黎曼 zeta 函数和某些 Artin L函数之间的零点抵消。为此,我们为拉普拉斯特征值 1/4 的 Maass 形式开发了一个逆定理,其中扭曲的L函数不被假定为完整的。我们不需要 Artin L函数的猜想自同构,只需要它们建立的亚纯延拓和泛函方程。

更新日期:2021-08-26
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