In this report we study the arithmetic of Rikuna’s generic polynomial for the cyclic group of order and obtain a generalized Kummer theory. It is useful under the condition that and where is a primitive -th root of unity and . In particular, this result with implies the classical Kummer theory. We also present a method for calculating not only the conductor but also the Artin symbols of the cyclic extension which is defined by the Rikuna polynomial.
Mots-clés : Generic polynomial, Kummer theory, Artin symbol
@article{AMBP_2009__16_1_127_0, author = {Komatsu, Toru}, title = {Generalized {Kummer} theory and its applications}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {127--138}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {16}, number = {1}, year = {2009}, doi = {10.5802/ambp.259}, zbl = {1188.11054}, mrnumber = {2514533}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.259/} }
TY - JOUR AU - Komatsu, Toru TI - Generalized Kummer theory and its applications JO - Annales mathématiques Blaise Pascal PY - 2009 SP - 127 EP - 138 VL - 16 IS - 1 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.259/ DO - 10.5802/ambp.259 LA - en ID - AMBP_2009__16_1_127_0 ER -
Komatsu, Toru. Generalized Kummer theory and its applications. Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 1, pp. 127-138. doi : 10.5802/ambp.259. http://www.numdam.org/articles/10.5802/ambp.259/
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