Bley, Burns and Hahn used relative algebraic K-theory methods to formulate a precise conjectural link 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. We provide concrete new evidence for this conjecture in the setting of extensions of odd prime-power degree by using a refined version of a well-known result of Ullom.

I would like to thank David Burns for suggesting the problem and many inspiring discussions. I am very grateful to Stéphane Vinatier for helpful, and encouraging, correspondence. Finally, I am very grateful to the anonymous referee for their careful review and valuable feedback, particularly, for having pointed out an error in an earlier version of the proof of Theorem 3.1 and for motivating me to obtain a sharper bound in the class group that is consistent with Vinatier's result.