Abstract
The well-known Birch and Swinnerton-Dyer conjecture gives a deep connection between the leading coefficient of the L-series and the arithmetic properties of an abelian variety. Both are very important and subtle. This paper is part of an effort to compute the analytic side explicitly in a special case. Indeed, we are interested in the central derivative of certain algebraic Hecke L-series, related to CM abelian varieties or more precisely pieces of it (CM motives). The result, together with the Gross-Zagier formula proved by Zhang ([Zh]), would also give a new way to compute the height of certain Heegner cycles on a Kuga-Sato variety. Let p ≡ 3 mod 4 be a prime number such that p > 3. Let k ≥ 0 be an integer. Let E = Q( √−p) and view it as a subfield of C such that √−p = i√p. Let hp be the ideal class number of E. A canonical Hecke character of E of weight 2k + 1 is a Hecke character μ satisfying
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.