Browsing by Author "Nica, Bogdan"

Now showing 1 - 3 of 3
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    Kloosterman sums over finite Frobenius rings
    (IMPAN, 2021) Nica, Bogdan; Mathematical Sciences, School of Science
    We 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.
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    On an identity of Sylvester
    (Elsevier, 2023-12) Nica, Bogdan; Mathematical Sciences, School of Science
    We discuss an algebraic identity, due to Sylvester, that is not as well-known as it should be.
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    On the independence number of regular graphs of matrix rings
    (Elsevier, 2024-01) Nica, Bogdan; Mathematical Sciences, School of Science
    Consider a graph on the non-singular matrices over a finite field, in which two distinct non-singular matrices are joined by an edge whenever their sum is singular. We prove an upper bound for the independence number of this graph. As a consequence, we obtain a lower bound for its chromatic number that significantly improves a previous result of Tomon.