Construction of Families of Imaginary Prime-Cyclotomic Integers With Prescribed Properties pp.37-53
Authors: (F. Thaine)
Abstract: Let m > 2 be an even integer. We develop a method to construct families of prime
numbers q = mf +1 with f odd, and of complex nonreal cyclotomic integers bq 2 Z[zq]
of degree m, with some prescribed properties, which are expressed as linear
combinations, over Z, of Gaussian periods. We apply that method in the construction
of families of numbers bq, as above, such that bqbq 2 Z. Some of those families bring
us families of cyclic difference sets. We also apply the method in the construction
of families of cyclic polynomials of degree m whose roots are complex nonreal qcyclotomic
integers with absolute norm q. This complements results of a previous
article where we show how to construct families of cyclic polynomials whose roots
are real q-cyclotomic units. We give several examples for small values of m, and a
MAPLE program that can be used to perform the calculations and to search for more
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