
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 eth 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 eth power residue group of p to form a difference set has been derived. The firstmentioned 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