Abstract
We conjecture a new bound on the exact denominators of the values at non-positive integers of imprimitive partial zeta functions associated with an Abelian extension of number fields. At s = 0, this conjecture is closely connected to a conjecture of David Hayes. We prove the new conjecture assuming that the Coates–Sinnott conjecture holds for the extension.
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Smith, B.R. Divisibility properties of values of partial zeta functions at non-positive integers. Math. Z. 270, 645–657 (2012). https://doi.org/10.1007/s00209-010-0817-z
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DOI: https://doi.org/10.1007/s00209-010-0817-z