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Fundam. Prikl. Mat., 2008, Volume 14, Issue 8, Pages 151–157 (Mi fpm1196)  

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

L. V. Kuz'min

Russian Research Centre "Kurchatov Institute"

Abstract: 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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English version:
Journal of Mathematical Sciences (New York), 2010, 166:5, 670–674

Bibliographic databases:

UDC: 519.4

Citation: L. V. Kuz'min, “On coherent families of uniformizing elements in some towers of Abelian extensions of local number fields”, Fundam. Prikl. Mat., 14:8 (2008), 151–157; J. Math. Sci., 166:5 (2010), 670–674

Citation in format AMSBIB
\Bibitem{Kuz08}
\by L.~V.~Kuz'min
\paper On coherent families of uniformizing elements in some towers of Abelian extensions of local number fields
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 8
\pages 151--157
\mathnet{http://mi.mathnet.ru/fpm1196}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2744940}
\elib{http://elibrary.ru/item.asp?id=12868947}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 166
\issue 5
\pages 670--674
\crossref{https://doi.org/10.1007/s10958-010-9882-4}
\elib{http://elibrary.ru/item.asp?id=15330349}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952292194}


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  • Фундаментальная и прикладная математика
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