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 $$p, we consider the
Lubin--Tate tower $K$_{p} = Ç
_{n ³ 0}
K_{n}, where $K$_{n} =
K(p_{n}),
$f($p_{0}) = 0,
and $f($p_{n+1}) =
p_{n}.
Here $f(X)$
defines the endomorphism $[$p] of the
Lubin--Tate group.
If $q$¹ 2,
then for any formal power series $g(X)$Î O_{K}[[X]]
the following equality holds:
$$å_{n = 0}^{¥}
Sp_{Kn/K} g(p_{n}) =
-g(0).
One has a similar equality in the case $q\; =\; 2$.

Location: http://mech.math.msu.su/~fpm/eng/k08/k088/k08809h.htm

Last modified: October 18, 2009