Reciprocity laws through formal groups

Oleg Demchenko*, Alexander Gurevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageAmerican English
Pages (from-to)1591-1596
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number5
StatePublished - 2013


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