Open Access
Sept. 2003 On Poincaré sums for local fields
Takashi Ono
Proc. Japan Acad. Ser. A Math. Sci. 79(7): 115-118 (Sept. 2003). DOI: 10.3792/pjaa.79.115


Let $K/k$ be a finite Galois extension of local fields. To each class $\gamma = [c]$ in $H^1(\operatorname{Gal}(K/k), U_K)$, $U_K$ being the group of units of $K$, we associate an index $i_\gamma(K/k) = (M_c : P_c)$ after the model of Poincaré series and study its relation to the ramification theory of $K/k$.


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Takashi Ono. "On Poincaré sums for local fields." Proc. Japan Acad. Ser. A Math. Sci. 79 (7) 115 - 118, Sept. 2003.


Published: Sept. 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1050.11099
MathSciNet: MR2008073
Digital Object Identifier: 10.3792/pjaa.79.115

Primary: 11F85

Keywords: $\mathfrak {p}$-adic fields , cohomology groups , Cyclotomic fields , differents , ramifications

Rights: Copyright © 2003 The Japan Academy

Vol.79 • No. 7 • Sept. 2003
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