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Full-Text Articles in Physical Sciences and Mathematics
Class Groups Of Quadratic Fields Ii, Duncan A. Buell
Class Groups Of Quadratic Fields Ii, Duncan A. Buell
Faculty Publications
A computation has been made of the noncyclic class groups of imaginary quadratic fields Q(√-D) for even and odd discriminants - D from 0 to - 25000000. Among the results are that 95% of the class groups are cyclic, and that -11203620 and -18397407 are the first discriminants of imaginary quadratic fields for which the class group has rank three in the 5-Sylow subgroup. The latter was known to be of rank three; this computation demonstrates that it is the first odd discriminant of 5-rank three or more.
Maximal Residue Difference Sets Modulo P, Duncan A. Buell, Kenneth S. Williams
Maximal Residue Difference Sets Modulo P, Duncan A. Buell, Kenneth S. Williams
Faculty Publications
Let p ≡ 1 (mod 4) be a prime. A residue difference set modulo p is a set S = {ai} of integers ai such that (ai/p) = +1 and ((ai - aj)/p) = +1 for all i and j with i ≠ j, where (n/p) is the Legendre symbol modulo p. Let mp be the cardinality of a maximal such set S. The authors estimate the size of mp.