Geodesic
On coherent families of uniformizing elements in some towers of Abelian extensions of local number fields
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 8, pp. 151-157
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For a local number field $K$ with the ring of integers $\mathcal O_K$, the residue field $\mathbb F_q$, and uniformizing $\pi$, we consider the Lubin–Tate tower $K_\pi=\bigcup_{n\geq0}K_n$, where $K_n=K(\pi_n)$, $f(\pi_0)=0$, and $f(\pi_{n+1})=\pi_n$. Here $f(X)$ defines the endomorphism $[\pi]$ of the Lubin–Tate group. If $q\neq2$, then for any formal power series $g(X)\in\mathcal O_K[[X]]$ the following equality holds: $\sum_{n=0}^\infty\mathrm{Sp}_{K_n/K}g(\pi_n)=-g(0)$. One has a similar equality in the case $q=2$. 
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     author = {L. V. Kuz'min},
     title = {On coherent families of uniformizing elements in some towers of {Abelian} extensions of local number fields},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {151--157},
     year = {2008},
     volume = {14},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a8/}
}
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L. V. Kuz'min. On coherent families of uniformizing elements in some towers of Abelian extensions of local number fields. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 8, pp. 151-157. http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a8/

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