Equidistribution of Rational Functions of Primes mod q

Given a prime number q and r(X) = f(X)/g(X), f, g ∈ ℤ [X], denote Ρ_r,q = {p prime : p ⩽ q, g(p) ≠ 0 (mod q)}. For r(X) not a linear polynomial we prove that the finite sequence U_r,q := { r(p) (mod q)/q: p ∈ P_r,q } becomes equidistributed mod 1 as q ⟶ ∞.

AMS (2000) Subject Classification. 11N69,11L07.