Moments in the Chebotarev density theorem: general class functions
Language
en
Document de travail - Pré-publication
English Abstract
In this paper we find lower bounds on higher moments of the error term in the Chebotarev density theorem. Inspired by the work of Bella\"{\i}che, we consider general class functions and prove bounds which depend on norms ...Read more >
In this paper we find lower bounds on higher moments of the error term in the Chebotarev density theorem. Inspired by the work of Bella\"{\i}che, we consider general class functions and prove bounds which depend on norms associated to these functions. Our bounds also involve the ramification and Galois theoretical information of the underlying extension $L/K$. Under a natural condition on class functions (which appeared in earlier work), we obtain that those moments are at least Gaussian. The key tools in our approach are the application of positivity in the explicit formula followed by combinatorics on zeros of Artin $L$-functions (which generalize previous work), as well as precise bounds on Artin conductors.Read less <
English Keywords
Chebotarev density theorem
Moment computations
Explicit formulae in arithmetic
Origin
Hal imported