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ON JACOBI SUMS AND DIFFERENCE SETS.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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
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