Variations on the theme of D. K. Faddeev’s paper “An explicit form of the Kummer–Takagi reciprocity law”
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S. V. Vostokov
Translated by: B. M. Bekker - St. Petersburg Math. J. 19 (2008), 719-722
- DOI: https://doi.org/10.1090/S1061-0022-08-01017-0
- Published electronically: June 25, 2008
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Abstract:
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 $\frac {a^{p-1}-1}{p}\cdot \underline {\alpha }’(1)\equiv 0\mod p$.References
- Gotthold Eisenstein, Mathematische Werke. Band II, Chelsea Publishing Co., New York, 1975. MR 0427030
- D. K. Faddeev, An explicit form of the Kummer-Takagi reciprocity law, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 1 (1966), 114–122 (Russian). MR 0219513
- Helmut Hasse, Zahlentheorie, Akademie-Verlag, Berlin, 1963 (German). Zweite erweiterte Auflage. MR 0153659
- S. V. Vostokov, The reciprocity law in an algebraic number field, Trudy Mat. Inst. Steklov. 148 (1978), 77–81, 273 (Russian). Algebra, number theory and their applications. MR 558942
Bibliographic Information
- S. V. Vostokov
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198504, Russia
- Email: sergeivostokov@mail.ru
- Received by editor(s): May 23, 2007
- Published electronically: June 25, 2008
- Additional Notes: Supported by INTAS
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 19 (2008), 719-722
- MSC (2000): Primary 11A15
- DOI: https://doi.org/10.1090/S1061-0022-08-01017-0
- MathSciNet review: 2381941
Dedicated: Dedicated to the centenary of the birth of my teacher Dmitriĭ Konstantinovich Faddeev