Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896929 | Journal of Number Theory | 2018 | 13 Pages |
Abstract
For an elliptic curve E/Q, Hasse's theorem asserts that #E(Fp)=p+1âap, where |ap|â¤2p. Assuming that E has complex multiplication, we establish asymptotics for primes p for which ap is in subintervals of the Hasse interval [â2p,2p] of measure o(p). In particular, given a function f=o(1) satisfying some mild conditions, we provide counting functions for primes p where |ap|â(2p(1âf(p)),2p), and for primes where apâ(2p(câf(p)),2cp), where câ(0,1) is a constant.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Anthony Agwu, Phillip Harris, Kevin James, Siddarth Kannan, Huixi Li,