ON JACOBI SUMS AND DIFFERENCE SETS.
Abstract
Let e be even and > or = 4, and let L be the cyclotomic field of the e-th roots of unity. Let J denote the group of Jacobi sums divisible by a certain prime ideal divisor P of a prime p = 1 (mod. e). Then J is embedded into a group J sub o = WXA, where W is the torsion group of L, and A is a free abelian group of rank phi(e)/2, quite independent of the primes p. On the other hand, a necessary and sufficient condition for an agglomerate of several cosets of the e-th power residue group of p to form a difference set has been derived. The first-mentioned theorem is then applied to this condition, to determine all the cyclic difference sets with prime moduli which have the multiplier group of index < or = 12. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1966
- Accession Number
- AD0648190
Entities
People
- Koichi Yamamoto
Organizations
- University of Wisconsin–Madison