Nonvanishing of Hecke L-Functions for CM Fields and Ranks of Abelian Varieties View Full Text


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Article Info

DATE

2011-06

AUTHORS

Riad Masri, Tonghai Yang

ABSTRACT

In this paper we prove a nonvanishing theorem for central values of L-functions associated to a large class of algebraic Hecke characters of CM number fields. A key ingredient in the proof is an asymptotic formula for the average of these central values. We combine the nonvanishing theorem with work of Tian and Zhang [TiZ] to deduce that infinitely many of the CM abelian varieties associated to these Hecke characters have Mordell–Weil rank zero. Included among these abelian varieties are higher-dimensional analogues of the elliptic -curves A(D) of B. Gross [Gr]. More... »

PAGES

648

References to SciGraph publications

  • 2002-09. The subconvexity problem for Artin L–functions in INVENTIONES MATHEMATICAE
  • 2010-10. Equidistribution of Heegner points and the partition function in MATHEMATISCHE ANNALEN
  • 2010-06. The subconvexity problem for GL2 in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1983. Complex Multiplication in NONE
  • 1999-07. Nonvanishing of central Hecke L-values and rank of certain elliptic curves in COMPOSITIO MATHEMATICA
  • 2011-02. Nonvanishing of Hecke L-functions and the Bloch–Kato conjecture in MATHEMATISCHE ANNALEN
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  • 2004-05. On CM abelian varieties over imaginary quadratic fields in MATHEMATISCHE ANNALEN
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  • 2006-02. CM-values of Hilbert modular functions in INVENTIONES MATHEMATICAE
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    http://scigraph.springernature.com/pub.10.1007/s00039-011-0121-z

    DOI

    http://dx.doi.org/10.1007/s00039-011-0121-z

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    https://app.dimensions.ai/details/publication/pub.1047055758


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