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

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -