Compositio Mathematica

Class Numbers of CM-Fields with Solvable Normal Closure

V. Kumar Murty a1
a1 Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, ON M5S 3G3, Canada

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Stark conjectured that given a positive integer h, there are only a finite number of CM-fields L with class number equal to h. We prove this conjecture for fields L of degree [gt-or-equal, slanted]6 whose normal closure is solvable.

Key Words: class number; CM field; Dedeking zeta function; Siegel zero.