Document Type

Post-Print

Publication Date

4-2010

Abstract

Fix a totally real number field F of degree at least 2. Under the assumptions of the generalized Riemann hypothesis and Artin's conjecture on the entirety of Artin L-functions, we derive an upper bound (in terms of the discriminant) on the class number of any CM number field with maximal real subfield F. This bound is a refinement of a bound established by Duke in 2001. Under the same hypotheses, we go on to prove that there exist infinitely many CM-extensions of F whose class numbers essentially meet this improved bound and whose Galois groups are as large as possible.

Document Object Identifier (DOI)

10.1016/j.jnt.2009.09.013

Publication Information

Journal of Number Theory

Included in

Mathematics Commons

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