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Item Kloosterman sums over finite Frobenius rings(IMPAN, 2021) Nica, Bogdan; Mathematical Sciences, School of ScienceWe study Kloosterman sums in a generalized ring-theoretic context, that of finite commutative Frobenius rings. We prove a number of identities for twisted Kloosterman sums, loosely clustered around moment computations. Our main result is the computation of the fourth moment of twisted Kloosterman sums, for non-primitive twists.