A refinement of the Stark conjectures over ATR fields

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Date

2025

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Abstract

We consider a number field K with exactly one complex embedding. In the 1970s, Starkconjectured formulas for the absolute values of units inside abelian extensions of K. We refine Stark’s conjectures with a proposed formula for the units themselves – not just their absolute values – by demonstrating a canonical decomposition of the smoothed partial zeta functions of K into conjugate pieces. We apply the techniques of 2009 work of Ren and Sczech, who worked in the case of cubic K.

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Dissertation

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Mathematics

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Mathematics, almost totally real, number theory, partial zeta functions, Shintani's method, smoothing, Stark conjectures

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https://hdl.handle.net/10161/34094

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https://creativecommons.org/licenses/by-nc-nd/4.0/

Citation

Black, Kairi (2025). A refinement of the Stark conjectures over ATR fields. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/34094.

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