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Equidistribution of Rational Functions of Primes mod q
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Given a prime number q and r(X) = f(X)/g(X), f, g ∈ ℤ [X], denote Ρr,q = {p prime : p ⩽ q, g(p) ≠ 0 (mod q)}. For r(X) not a linear polynomial we prove that the finite sequence Ur,q := { r(p) (mod q)/q: p ∈ Pr,q } becomes equidistributed mod 1 as q ⟶ ∞.
AMS (2000) Subject Classification. 11N69,11L07.
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