On a Refined Stark Conjecture for Function Fields

  title={On a Refined Stark Conjecture for Function Fields},
  author={Cristian Dinu Popescu},
Let LK/k(s, χ) be the ArtinL-function associated to a finite, Galois extensions of global fieldsK/k, and a character χ ∈ Ĝ(K/k). In the 1970’s and early 1980’s, Stark [15] developed a conjecture concerning the leading coefficient of the Taylor expansion of LK/k(s, χ), at s = 0. The classical formulae for the case of a Dedekind Zeta-function provide good hints: if the order of vanishing is r, then the coefficient in question should be a rational number multiplied by a regulator, obtained as a… CONTINUE READING
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