Add to ORKGInternational audienceHooley proved that if f ∈ Z[X] is irreducible of degree ≥ 2, then the fractions {r/n}, 0 < r < n with f (r) ≡ 0 (mod n), are uniformly distributed in ]0, 1[. In this paper we study such problems for reducible polynomials of degree 2 and 3 and for finite products of linear factors. In particular, we establish asymptotic formulas for exponential sums over these normalized roots
AbstractThe asymptotic distribution of the roots of the congruence ax ≡ b (mod D), 1 ≤ x ≤ D, as D v...
In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer...
Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential sums associate...
AbstractWe obtain estimates of complete rational exponentials sums with sparse polynomials and ratio...
AbstractFor a fixed integer s≥2, we estimate exponential sums with alternative power sums As(n)=∑i=0...
We obtain new bounds of exponential sums modulo a prime p with binomials axk + bxn. In particular, ...
This is a preprint of an article published in the Canadian Journal of Mathematics, 55 (2003), pp.225...
AbstractThe following theorem is proved. Suppose that for integers r,s⩾2, f(x,y) is an inhomogeneous...
We give a purity result for exponential sums of the type P x∈kn ψ(f(x)), where k is a finite field ...
AbstractWe give new bounds of exponential sums with sequences of iterations of Dickson polynomials o...
AbstractWe consider incomplete exponential sums in several variables of the form S(f,n,m)=12n∑x1∈{-1...
AbstractLet Fq[X] denote the multiplicative semigroups of monic polynomials in one indeterminate X, ...
We combine two of Igusa's conjectures with recent semi-continuity results by Musta\c{t}\u{a} and Pop...
AbstractIn this paper exponential sums of the type Y1ew1x+Y2ew2x+…+Ynewnx where w1, w2 …, wn are pai...
AbstractFor a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of ...
AbstractThe asymptotic distribution of the roots of the congruence ax ≡ b (mod D), 1 ≤ x ≤ D, as D v...
In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer...
Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential sums associate...
AbstractWe obtain estimates of complete rational exponentials sums with sparse polynomials and ratio...
AbstractFor a fixed integer s≥2, we estimate exponential sums with alternative power sums As(n)=∑i=0...
We obtain new bounds of exponential sums modulo a prime p with binomials axk + bxn. In particular, ...
This is a preprint of an article published in the Canadian Journal of Mathematics, 55 (2003), pp.225...
AbstractThe following theorem is proved. Suppose that for integers r,s⩾2, f(x,y) is an inhomogeneous...
We give a purity result for exponential sums of the type P x∈kn ψ(f(x)), where k is a finite field ...
AbstractWe give new bounds of exponential sums with sequences of iterations of Dickson polynomials o...
AbstractWe consider incomplete exponential sums in several variables of the form S(f,n,m)=12n∑x1∈{-1...
AbstractLet Fq[X] denote the multiplicative semigroups of monic polynomials in one indeterminate X, ...
We combine two of Igusa's conjectures with recent semi-continuity results by Musta\c{t}\u{a} and Pop...
AbstractIn this paper exponential sums of the type Y1ew1x+Y2ew2x+…+Ynewnx where w1, w2 …, wn are pai...
AbstractFor a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of ...
AbstractThe asymptotic distribution of the roots of the congruence ax ≡ b (mod D), 1 ≤ x ≤ D, as D v...
In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer...
Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential sums associate...