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The smallest prime in a conjugacy class and the first sign change for automorphic 𝐿-functions
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-12-31 , DOI: 10.1090/proc/15233 Peter Cho , Henry Kim
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-12-31 , DOI: 10.1090/proc/15233 Peter Cho , Henry Kim
Abstract:Let 
be an 
-field. For a nonidentity conjugacy class 
, define 
to be the smallest prime 
such that Frob
. By using the observation that 
is interpreted as the first prime sign change of the Dirichlet coefficients of automorphic 
-functions, we improve the known bound on 
for 
. (For 
, we need to assume the strong Artin conjecture.)
中文翻译：
共轭类中最小的素数和自守𝐿函数的第一个符号变化
摘要：让我们成为一个领域。对于非身份共轭类，将其定义为最小的素数，例如Frob 。通过使用观察被解释为自守的狄氏系数的第一任符号改变-functions，我们改进了已有的约束上的。（对于，我们需要假设强烈的Artin猜想。）
更新日期：2021-02-08
be an -field. For a nonidentity conjugacy class , define to be the smallest prime such that Frob. By using the observation that is interpreted as the first prime sign change of the Dirichlet coefficients of automorphic -functions, we improve the known bound on for . (For , we need to assume the strong Artin conjecture.) 中文翻译：
共轭类中最小的素数和自守𝐿函数的第一个符号变化
摘要：让我们
成为一个领域。对于非身份共轭类，将其定义为最小的素数，例如Frob 。通过使用观察被解释为自守的狄氏系数的第一任符号改变-functions，我们改进了已有的约束上的。（对于，我们需要假设强烈的Artin猜想。）
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