Abstract
Given an elliptic curve E defined over and a prime p of good reduction, let denote the group of -points of the reduction of E modulo p, and let ep denote the exponent of this group. Assuming a certain form of the generalized Riemann hypothesis (GRH), we study the average of ep as ranges over primes of good reduction, and find that the average exponent essentially equals p⋅cE, where the constant cE>0 depends on E. For E without complex multiplication (CM), cE can be written as a rational number (depending on E) times a universal constant, , the product being over all primes q. Without assuming GRH, we can determine the average exponent when E has CM, as well as give an upper bound on the average in the non-CM case.
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.
