by Titus Piezas III
ABSTRACT: By a series of quadratic Tschirnhausen transformations, the general quintic can be transformed into the solvable De Moivre quintic. The last step, naturally enough, involves solving a resolvent sextic which turns out to be: a) a polynomial identical to a formula for the j-function in terms of Dedekind eta quotients, and b) the Jacobi sextic in disguise. As a side effect, it gives the complete parametrization of solvable Brioschi quintics with rational coefficients. In addition, solutions of other one-parameter quintics will also be discussed.
Mathematics Subject Classification: Primary: 12E12.
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