چكيده فارسي :
For a prime p and fixed integers a and b, let n(p) be the number of solutions (x, y) of the
cubic $y^{2} = x^{3} + ax + b$ over the finite field Fp and let $a(p) = p − n(p)$. In 1976, Serge Lang and
Hale Trotter formulated a conjecture regarding the distribution of primes p for which a(p) = A
for a fixed integer A. This conjecture is widely open. In this talk we give an exposition of this
conjecture and describe some of the work done in this topic over the last few decades. We also
report on our recent joint work with James Parks (KTH Royal Institute of Technology-Sweden)
on a version of this conjecture for two cubics (elliptic curves).
