Let p be an odd prime,and n,k be nonnegative integers.Let Dn,k(1,x)be the reversed Dickson polynomial of the(k+1)-th kind.In this paper,by using Hermite's criterion,we study the permutational properties of the rev...Let p be an odd prime,and n,k be nonnegative integers.Let Dn,k(1,x)be the reversed Dickson polynomial of the(k+1)-th kind.In this paper,by using Hermite's criterion,we study the permutational properties of the reversed Dickson polynomials Dn,k(1,x)over finite fields in the case of n=mp* with 0<m<p-1.In particular,we provide some precise characterizations for Dn,k(1,x)being permutation polynomials over finite fields with characteristic p when n=2p^(s),or n=3p^(s),or n=4p^(s).展开更多
Let F_(q) be a finite field and F_(q)^(s) be an extension of F_(q).Let f(x)∈F_(q)[x]be a polynomial of degree n with g c d(n,q)=1.We present a recursive formula for evaluating the exponential sum∑c∈F_(q)^(s)χ^((s)...Let F_(q) be a finite field and F_(q)^(s) be an extension of F_(q).Let f(x)∈F_(q)[x]be a polynomial of degree n with g c d(n,q)=1.We present a recursive formula for evaluating the exponential sum∑c∈F_(q)^(s)χ^((s))(f(x)).Let a and b be two elements in F_(q) with a a≠0,u be a positive integer.We obtain an estimate for the exponential sum∑c∈F^(∗)_(q)^(s)χ^((s))(ac^(u)+bc^(−1)),whereχ^((s))is the lifting of an additive characterχof F_(q).Some properties of the sequences constructed from these exponential sums are provided too.展开更多
基金supported by National Natural Science Foundation of China(No.12226335)by China's Central Government Funds for Guiding Local Scientific and Technological Development(No.2021ZYD0013).
文摘Let p be an odd prime,and n,k be nonnegative integers.Let Dn,k(1,x)be the reversed Dickson polynomial of the(k+1)-th kind.In this paper,by using Hermite's criterion,we study the permutational properties of the reversed Dickson polynomials Dn,k(1,x)over finite fields in the case of n=mp* with 0<m<p-1.In particular,we provide some precise characterizations for Dn,k(1,x)being permutation polynomials over finite fields with characteristic p when n=2p^(s),or n=3p^(s),or n=4p^(s).
文摘Let F_(q) be a finite field and F_(q)^(s) be an extension of F_(q).Let f(x)∈F_(q)[x]be a polynomial of degree n with g c d(n,q)=1.We present a recursive formula for evaluating the exponential sum∑c∈F_(q)^(s)χ^((s))(f(x)).Let a and b be two elements in F_(q) with a a≠0,u be a positive integer.We obtain an estimate for the exponential sum∑c∈F^(∗)_(q)^(s)χ^((s))(ac^(u)+bc^(−1)),whereχ^((s))is the lifting of an additive characterχof F_(q).Some properties of the sequences constructed from these exponential sums are provided too.
