Non-vanishing of Carlitz-fermat Quotients modulo Primes
نویسندگان
چکیده
Contents 1. Introduction 1 2. Carlitz-Fermat quotients 2 3. Non-vanishing of Carlitz-Fermat quotients modulo primes 4 1. Introduction. Let q = p s , where p is a prime and s is a positive integer. Let F q be the finite field of q elements, and set A = F q [T ] and k = F q (T). Let τ be the mapping defined by τ (x) = x q , and let kτ denote the twisted polynomial ring. Let C : A → kτ (a → C a) be the Carlitz module, namely, C be an F q-algebra homomorphism such that C T = T + τ. Let R be any commutative k-algebra. The definition of the Carlitz module C implies that C T (a) = T a + a q for every a ∈ R.
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