Abstract
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 language | American English |
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Pages (from-to) | 1591-1596 |
Number of pages | 6 |
Journal | Proceedings of the American Mathematical Society |
Volume | 141 |
Issue number | 5 |
DOIs | |
State | Published - 2013 |