FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 8, PAGES 151-157

On coherent families of uniformizing elements in some towers of Abelian extensions of local number fields

L. V. Kuz'min

Abstract

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For a local number field $K$ with the ring of integers $O$_K, the residue field $F$_q, and uniformizing $$p, we consider the Lubin--Tate tower $K$_p = Ç _{n ³ 0} K_n, where $K$_n = K(p_n), $f($p₀) = 0, and $f($p_n+1) = p_n. Here $f(X)$ defines the endomorphism $[$p] of the Lubin--Tate group. If $q$¹ 2, then for any formal power series $g(X)$Î O_K[[X]] the following equality holds: $$å_{n = 0}^¥ Sp_Kn/K g(p_n) = -g(0). One has a similar equality in the case $q\; =\; 2$.

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Last modified: October 18, 2009