Hall 123

Poisson Distribution of a Prime Counting Function Corresponding to Elliptic Curves

Sumit Giri

IMSc

Let E be an elliptic curve defined over rational field Q and N be a positive integer. Now M_E(N) denotes the number of primes p, such that the group E_p(F_p) is of order N. We shall give heuristic on the behavior of the function. Also note down some the recent development on this aspect. No prerequisite is required.