论文标题
在Galois-Gauss总和和逆不同的平方根上
On Galois-Gauss sums and the square root of the inverse different
论文作者
论文摘要
We discuss a possible generalisation of a conjecture of Bley, Burns and Hahn concerning the relation between the second Adams-operator twisted Galois-Gauss sums of weakly ramified Artin characters and the square root of the inverse different of finite, odd degree, Galois extensions of number fields, to the setting of all finite Galois extensions of number fields for which a square root of the inverse different exists.我们还将Bley，Burns和Hahn的关键方法和结果扩展到了这个更一般的环境，并通过将这些方法与Agboola，Burns，Caputo和本作者结合起来，将这些方法与Artin twisted disted discted norsbleclublectiblectimectic角色有关，我们为Erez Confersing Erez Confersing galois结构的构想提供了新的洞察力。
We discuss a possible generalisation of a conjecture of Bley, Burns and Hahn concerning the relation between the second Adams-operator twisted Galois-Gauss sums of weakly ramified Artin characters and the square root of the inverse different of finite, odd degree, Galois extensions of number fields, to the setting of all finite Galois extensions of number fields for which a square root of the inverse different exists. We also extend the key methods and results of Bley, Burns and Hahn to this more general setting and, by combining these methods with a recent result of Agboola, Burns, Caputo and the present author concerning Artin root numbers of twisted irreducible symplectic characters, we provide new insight into a conjecture of Erez concerning the Galois structure of the square root of the inverse different.
