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2 results

  • A class number formula for higher derivatives of abelian L-functions

  • A. Hayward
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 1 / January 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 99-129
    Print publication:
    January 2004
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  • Gross and Rubin have made conjectures about special values of equivariant L-functions associated to abelian extensions of global fields. We describe a common refinement, due to Burns, and give evidence in favour of this conjecture for quadratic extensions and cyclotomic fields. We also note that the statement provides a new interpretation of further conjectures of Darmon and Gross.

  • Stickelberger Elements for Cyclic Extensions and the Order of Vanishing of Abelian L-Functions at s=0

  • Joongul Lee
  • Journal:
    Compositio Mathematica / Volume 138 / Issue 2 / September 2003
    Published online by Cambridge University Press:
    04 December 2007, pp. 157-163
    Print publication:
    September 2003
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  • We study the Stickelberger element of a cyclic extension of global fields of prime power degree. Assuming that S contains an almost splitting place, we show that the Stickelberger element is contained in a power of the relative augmentation ideal whose exponent is at least as large as Gross's prediction. This generalizes the work of Tate (see Section 4) on a refinement of Gross's conjecture in the cyclic case. We also present an example for which Tate's prediction does not hold.