Add to ORKGLet F = GF(q) denote the finite field with q =2nelements. For f(X)∈f[X] we let (formula presented) A deep result of Carlitz and Uchiyama states that if f(X)≠g(X)2+g(X)+b, g(X)∈F[X], b∈F, then │S(f)│≦(deg f-1)q1/2.then This estimate is proved in an elementary way when deg f = 3, 4, 5 or 6. In certain cases the estimate is improved
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. W...
International audienceIn Fq, Dartyge and Sarkozy introduced the notion of digits and studied some pr...
International audienceLet F be a finite field with q elements (q odd), Q is an element of F[T] and f...
AbstractLet A=Fq[t] denote the ring of polynomials over the finite field Fq. We denote by e a certai...
AbstractWe give estimates of two exponential sums over finite fields for which Weil's estimates fail...
AbstractWe generalize the constructon of F. R. Chung of graphs from finite fields and estimate their...
AbstractIn this paper, bounds for exponential sums associated to polynomial ƒ defined over finite fi...
We prove explicit formulas for certain first and second moment sums of families of Gaussian hypergeo...
AbstractLet N be the number of solutions of the equationx1m1+⋯+xnmn=ax1⋯xn over the finite field Fq=...
AbstractWe prove a general identity for a F23 hypergeometric function over a finite field Fq, where ...
Let Fp be the finite field of a prime order p. Let F: Fp x Fp --> Fp be a function defined by F(x, y...
The goal of the thesis is to understand Stepanov’s method, which is used to prove in an elementary w...
Notes for a talk given at LSBU on 7 September 2007 Finite fields Fq is the finite field of q element...
AbstractLet F denote a finite field with q=pf elements, and let σ(A) equal the trace of the square m...
We extend to the setting of polynomials over a finite field certain estimates for short Kloosterman ...
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. W...
International audienceIn Fq, Dartyge and Sarkozy introduced the notion of digits and studied some pr...
International audienceLet F be a finite field with q elements (q odd), Q is an element of F[T] and f...
AbstractLet A=Fq[t] denote the ring of polynomials over the finite field Fq. We denote by e a certai...
AbstractWe give estimates of two exponential sums over finite fields for which Weil's estimates fail...
AbstractWe generalize the constructon of F. R. Chung of graphs from finite fields and estimate their...
AbstractIn this paper, bounds for exponential sums associated to polynomial ƒ defined over finite fi...
We prove explicit formulas for certain first and second moment sums of families of Gaussian hypergeo...
AbstractLet N be the number of solutions of the equationx1m1+⋯+xnmn=ax1⋯xn over the finite field Fq=...
AbstractWe prove a general identity for a F23 hypergeometric function over a finite field Fq, where ...
Let Fp be the finite field of a prime order p. Let F: Fp x Fp --> Fp be a function defined by F(x, y...
The goal of the thesis is to understand Stepanov’s method, which is used to prove in an elementary w...
Notes for a talk given at LSBU on 7 September 2007 Finite fields Fq is the finite field of q element...
AbstractLet F denote a finite field with q=pf elements, and let σ(A) equal the trace of the square m...
We extend to the setting of polynomials over a finite field certain estimates for short Kloosterman ...
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. W...
International audienceIn Fq, Dartyge and Sarkozy introduced the notion of digits and studied some pr...
International audienceLet F be a finite field with q elements (q odd), Q is an element of F[T] and f...