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Stark's conjecture in multi-quadratic extensions, revisited

David S. DummitJonathan W. SandsBrett Tangedal — 2003

Journal de théorie des nombres de Bordeaux

Stark’s conjectures connect special units in number fields with special values of L -functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent 2 . For biquadratic extensions and most others, we prove more, establishing the conjecture in full.

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