TY - JOUR
T1 - Reciprocity laws through formal groups
AU - Demchenko, Oleg
AU - Gurevich, Alexander
PY - 2013
Y1 - 2013
N2 - A relation between formal groups and reciprocity laws is studied following the approach initiated by Honda. Let ξ denote an mth primitive root of unity. For a character χ of order m, we define two one-dimensional formal groups over Z[ξ] and prove the existence of an integral homomorphism between them with linear coefficient equal to the Gauss sum of χ. This allows us to deduce a reciprocity formula for the mth residue symbol which, in particular, implies the cubic reciprocity law.
AB - A relation between formal groups and reciprocity laws is studied following the approach initiated by Honda. Let ξ denote an mth primitive root of unity. For a character χ of order m, we define two one-dimensional formal groups over Z[ξ] and prove the existence of an integral homomorphism between them with linear coefficient equal to the Gauss sum of χ. This allows us to deduce a reciprocity formula for the mth residue symbol which, in particular, implies the cubic reciprocity law.
UR - http://www.scopus.com/inward/record.url?scp=84874219972&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2012-11632-6
DO - 10.1090/S0002-9939-2012-11632-6
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AN - SCOPUS:84874219972
SN - 0002-9939
VL - 141
SP - 1591
EP - 1596
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 5
ER -