Nonvanishing of Hecke L-Functions for CM Fields and Ranks of Abelian Varieties Academic Article

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]. 2011 Springer Basel AG.

authors

• Masri, Mohamad

published proceedings

• GEOMETRIC AND FUNCTIONAL ANALYSIS

author list (cited authors)

• Masri, R., & Yang, T.

citation count

• 2

complete list of authors

• Masri, Riad||Yang, Tonghai

publication date

• June 2011

publisher

• Springer Nature  Publisher

keywords

• Cm Abelian Variety
• Equidistribution
• L-function
• Mordell-weil Rank

Digital Object Identifier (DOI)

• 10.1007/s00039-011-0121-z

start page

• 648

end page

• 679

volume

• 21

issue

• 3

URL

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