Let be a finite extension of . The field of norms of a -adic Lie extension is a local field of characteristic which comes equipped with an action of . When can we lift this action to characteristic , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of -modules, and give a condition for the existence of certain types of lifts.
A limit theorem in the space of continuous functions for the Dirichlet polynomialwhere denote the coefficients of the Dirichlet series expansion of the function in the half-plane
A limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for the Estermann zeta-function is obtained.
In this paper two weighted functional limit theorems for the function introduced by K. Matsumoto are proved.
We prove a limit theorem in the space of analytic functions for the Hurwitz zeta-function with algebraic irrational parameter.
We consider the ensemble of curves {γα, N: α∈(0, 1], N∈ℕ} obtained by linearly interpolating the values of the normalized theta sum N−1/2∑n=0N'−1exp(πin2α), 0≤N'<N. We prove the existence of limiting finite-dimensional distributions for such curves as N→∞, when α is distributed according to any probability measure λ, absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [Duke Math. J.97 (1999) 127–153] and Jurkat and van Horne [Duke...