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:

1966-09-01

Pagination or Media Count:

55.0

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 phie2, 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