PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On Galois–Gauss sumsand the square root of the inverse different

Volume 209 / 2023

Yu Kuang Acta Arithmetica 209 (2023), 319-355 MSC: Primary 11R33; Secondary 16E20, 19A31. DOI: 10.4064/aa220626-3-7 Published online: 3 October 2023


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.


  • Yu KuangSchool of Mathematical Sciences
    Shanghai Jiao Tong University
    Shanghai 200240, China

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image