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Li coefficients for automorphic L -functions

Jeffrey C. Lagarias (2007)

Annales de l’institut Fourier

Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients λ n ( n = 1 , 2 , ...

Lifting the field of norms

Laurent Berger (2014)

Journal de l’École polytechnique — Mathématiques

Let K be a finite extension of Q p . The field of norms of a p -adic Lie extension K / K is a local field of characteristic p which comes equipped with an action of Gal ( K / K ) . When can we lift this action to characteristic 0 , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of ( ϕ , Γ ) -modules, and give a condition for the existence of certain types of lifts.

Local Class Field Theory via Lubin-Tate Theory

Teruyoshi Yoshida (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].

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