Abstract
This article relates the Gross-Zagier formula with a simpler formula of Gross for special values of L -series, via the theory of congruences between modular forms. Given two modular forms f and g (of different levels) which are congruent but whose functional equations have sign -1 and 1 respectively, and an imaginary quadratic field K satisfying certain auxiliary conditions, the main result gives a congruence between the algebraic part of L '( f/K , 1) (expressed in terms of Heegner points) and the algebraic part of the special value L ( g / K , 1). Congruences of this type were anticipated by Jochnowitz, and for this reason are referred to as "Jochnowitz congruences."
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
