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A Chebotarev density theorem for certain families of D_4-quartic fields

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Monday, October 01, 2018
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12:00 pm - 1:00 pm
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Chen An
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Graduate/Faculty Seminar

In a recent paper of Pierce, Turnage-Butterbaugh, and Wood, the authors proved an effective Chebotarev density theorem for families of number fields. Notably D_4-quartic fields have not been treated in their paper. In this talk, I will explain the importance of the case for D_4-quartic fields and will present my proof of a Chebotarev density theorem for certain families of D_4-quartic fields. The key tools are a lower bound for the number of fields in the families and a zero-free region for almost all fields in the families.