Non-vanishing of the Central Derivative of Canonical Hecke L-functions

نویسندگان

  • Stephen D. Miller
  • Tonghai Yang
چکیده

Every Hecke character of K satisfying (1.1) and (1.2) is actually a quadratic twist of a canonical Hecke character (see Section 2 for a precise description of these characters and which fields have them). Let L(s, χ) denote the Hecke L-function of χ, and Λ(s, χ) its completion; Λ(s, χ) satisfies the functional equation Λ(s, χ) = W (χ)Λ(2 − s, χ), where W (χ) = ±1 is the root number. If χ is a canonical Hecke character with W (χ) = 1, then the central value Λ(1, χ) 6= 0 by a theorem of Montgomery and Rohrlich [MR]. Of course, it automatically vanishes when W (χ) = −1 by the functional equation. The main result of this paper is

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تاریخ انتشار 2000