Accession Number : AD0648190

Title :   ON JACOBI SUMS AND DIFFERENCE SETS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Yamamoto,Koichi

Report Date : SEP 1966

Pagination or Media Count : 55

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)

Descriptors :   (*COMBINATORIAL ANALYSIS, *SET THEORY), PRIME NUMBERS, NUMBER THEORY, ALGEBRA, GROUPS(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE