AbstractAn asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb
Let $X$ be a large integer. We prove that, for any fixed positive integer $k$, a suitable asymptotic...
We give an exact coefficients formula of any infinite product of power series with constant term equ...
AbstractLet Gq denote the multiplicative semigroup of all monic polynomials in one indeterminate ove...
AbstractAn asymptotic formula is obtained for the number of representations of an element of a finit...
Subject to the Riemann hypothesis for Dirichlet L-functions an asymptotic formula is obtained for th...
AbstractLet Fr denote a finite field with r elements. Let q be a power of a prime, and p1,p2, p3 be ...
We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a line...
A $k$-representation of an integer $\l$ is a representation of $\l$ as sum of $k$ powers of $2$, whe...
We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a l...
AbstractLet k⩾5 be an integer, and let x⩾1 be an arbitrary real number. We derive a boundOε,k(x2/3k+...
As an application of Faulhaber’s theorem on sums of powers of integers and the associated Faulhaber...
For each odd prime power q, and each integer k, we determine the sum of the k-th powers of all eleme...
AbstractLet Fr denote a finite field with r elements. Let q be a power of a prime, and p1,p2, p3 be ...
Let $X$ be a large integer. We prove that, for any fixed positive integer $k$, a suitable asymptotic...
We give an exact coefficients formula of any infinite product of power series with constant term equ...
Let $X$ be a large integer. We prove that, for any fixed positive integer $k$, a suitable asymptotic...
We give an exact coefficients formula of any infinite product of power series with constant term equ...
AbstractLet Gq denote the multiplicative semigroup of all monic polynomials in one indeterminate ove...
AbstractAn asymptotic formula is obtained for the number of representations of an element of a finit...
Subject to the Riemann hypothesis for Dirichlet L-functions an asymptotic formula is obtained for th...
AbstractLet Fr denote a finite field with r elements. Let q be a power of a prime, and p1,p2, p3 be ...
We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a line...
A $k$-representation of an integer $\l$ is a representation of $\l$ as sum of $k$ powers of $2$, whe...
We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a l...
AbstractLet k⩾5 be an integer, and let x⩾1 be an arbitrary real number. We derive a boundOε,k(x2/3k+...
As an application of Faulhaber’s theorem on sums of powers of integers and the associated Faulhaber...
For each odd prime power q, and each integer k, we determine the sum of the k-th powers of all eleme...
AbstractLet Fr denote a finite field with r elements. Let q be a power of a prime, and p1,p2, p3 be ...
Let $X$ be a large integer. We prove that, for any fixed positive integer $k$, a suitable asymptotic...
We give an exact coefficients formula of any infinite product of power series with constant term equ...
Let $X$ be a large integer. We prove that, for any fixed positive integer $k$, a suitable asymptotic...
We give an exact coefficients formula of any infinite product of power series with constant term equ...
AbstractLet Gq denote the multiplicative semigroup of all monic polynomials in one indeterminate ove...
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