Theoretical Statistics and Mathematics Unit, ISI Delhi

October 26, 2016 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Sumit Giri,
Tel Aviv University Israel

Title:
Short average distribution of a prime counting function over families of elliptic curves

Abstract of Talk

Let E be an elliptic curve defined over Q and let N be a
positive integer. Now, M_E(N) counts the number of primes p such that the
group E_p(F_p) is of order N. In an earlier joint work with
Balasubramanian, we showed that M_E(N) follows Poisson distribution when an
average is taken over a family of elliptic curve with parameters A and B
where A, B > N^{l/2} (log N)^{1+\gamma} and $AB>N^{3l/2}(\log N)^{2+\gamma}
for a fixed integer l and any \gamma>0. In this talk, we explain that the
same result holds even if we take A and B in the range \exp(N^{\epsilon^2
/20l})> A, B>N^\epsilon and AB>N^{3l/2}(log N)^{6+\gamma} for any
\epsilon>0.