DE LA BRETÈCHE, Régis; FIORILLI, Daniel; JOUVE, Florent

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DE LA BRETÈCHE, Régis
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]

FIORILLI, Daniel
Laboratoire de Mathématiques d'Orsay [LMO]

JOUVE, Florent
Institut de Mathématiques de Bordeaux [IMB]

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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.< Leer menos

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Chebotarev density theorem

Moment computations

Explicit formulae in arithmetic

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Moments in the Chebotarev density theorem: general class functions

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