Blair K. Spearman

CHARACTERIZATION OF SOLVABLE QUINTICS X5 + AX + B

(1994). Characterization of Solvable Quintics x5 + ax + b. The American Mathematical Monthly: Vol. 101, No. 10, pp. 986-992.

DIHEDRAL QUINTIC FIELDS WITH A POWER BASIS

to be monogenic. Dummit and Kisilevsky[4] have shown that there exist infinitely many cyclic cubic fields whichare monogenic. The same has been shown for non-cyclic cubic fields, purequartic fields, bicyclic quartic fields, dihedral quartic fields by Spearman andWilliams [15], Funakura [6], Nakahara [14], Huard, Spearman and Williams[10] respectively. It is not known if there are infinitely many monogeniccyclic quartic fields. If

The conductor of a cyclic quartic field using Gauss sums

AbstractLet Q denote the field of rational numbers. Let K be a cyclic quartic extension of Q. It is known that there are unique integers A, B, C, D such that

Cyclic Cubic Fields of Given Conductor and Given Index

K = Q\left( {\sqrt {A(D + B\sqrt D )} } \right)

Representing primes by binary quadratic forms

where A is squarefree and odd, D=B2+C2 is squarefree, B

Cyclic sextic trinomials x6 + Ax + B

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