Variations on the theme of D. K. Faddeev's paper “An explicit form of the Kummer–Takagi reciprocity law”
Algebra i analiz, Tome 19 (2007) no. 5, pp. 65-69
Cet article a éte moissonné depuis la source Math-Net.Ru
The following form of the Eisenstein reciprocity law is established: in the cyclotomic field $\mathbb{Q}(\zeta)$, the relation $(\frac{\alpha}{a})=(\frac{a}{\alpha})$ is equivalent to $\frac{a^{p-1}-1}{p}\cdot \underline{\alpha}'(1)\equiv 0\mod p$.
Keywords:
Reciprocity law, cyclotomic field.
@article{AA_2007_19_5_a2,
author = {S. V. Vostokov},
title = {Variations on the theme of {D.} {K.~Faddeev's} paper {{\textquotedblleft}An} explicit form of the {Kummer{\textendash}Takagi} reciprocity law{\textquotedblright}},
journal = {Algebra i analiz},
pages = {65--69},
year = {2007},
volume = {19},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AA_2007_19_5_a2/}
}
S. V. Vostokov. Variations on the theme of D. K. Faddeev's paper “An explicit form of the Kummer–Takagi reciprocity law”. Algebra i analiz, Tome 19 (2007) no. 5, pp. 65-69. http://geodesic.mathdoc.fr/item/AA_2007_19_5_a2/
[1] Eisenstein G., “Beweis des allgemeinsten Reziprozitaetsgesetze zwischen rellen und komplexen Zahlen”, Mathematische Werke, Band II, Chelsea, New York, 1975, 189–198 | MR
[2] Faddeev D. K., “K yavnoi forme zakona vzaimnosti Kummera–Takagi”, Zap. nauchn. sem. LOMI, 1, 1966, 114–122 | MR | Zbl
[3] Hasse H., Zahlentheorie, Akademie-Verlag, Berlin, 1963 | MR | Zbl
[4] Vostokov S. V., “K zakonu vzaimnosti polya algebraicheskikh chisel”, Tr. Mat. in-ta AN SSSR, 148, 1978, 77–81 | MR | Zbl