The number of roots of polynomials of large degree in a prime field
  We establish asymptotic upper bounds on the number of zeros modulo $p$ of certain polynomials with integer coefficients, with $p$ prime numbers arbitrarily large. The polynomials we consider have degree of size $p$ and are obtained by truncating certain power series with rational coefficients that satisfy simple differential equations. 
Amit Ghosh and Kenneth Ward
math.NT