Add to ORKGLet g be a primitive root modulo a prime p. It is proved that the triples (gx, gy, gxy), x, yfl 1, … , pfi1, are uniformly distributed modulo p in the sense of H. Weyl. This result is based on the following upper bound for double exponential sums. Let e " 0 be fixed. Then 3 p−" x,y=" exp02pi agx›bgy›cgxyp 1flO(p$"/"’+e) uniformly for any integers a, b, c with gcd(a, b, c, p)fl 1. Incomplete sums are estimated as well. The question is motivated by the assumption, often made in cryptography, that the triples (gx, gy, gxy) cannot be distinguished from totally random triples in feasible computation time. The results imply that this is in any case true for a constant fraction of the most significant bits, and for a const...
AbstractFor a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of ...
summary:A positive integer $n$ is called a square-free number if it is not divisible by a perfect sq...
An x-pseudopower to base g is a positive integer which is not a power of g yet is so modulo p for al...
Let g be a primitive root modulo a prime p. It is proved that the triples (gx, gy, gxy), x, yfl 1, …...
Let Fp be a prime field of p elements and let g be an element of Fp of multiplicative order t modulo...
Let g be a primitive root modulo a (n+1)-bit prime p. In this paper we prove the uniformity of distr...
http://www.math.missouri.edu/~bbanks/papers/index.htmlLet p be a prime and 79 an integer of order t ...
Abstract. Let p be a prime and V an integer of order t in the multiplicative group modulo p. In this...
AbstractFor a fixed integer s≥2, we estimate exponential sums with alternative power sums As(n)=∑i=0...
For a fixed integer s ≥ 1, we estimate exponential sums with harmonic sums [equation omitted for for...
Let m = pl be a product of two distinct primes p and l. We show that for almost all exponents e with...
We study the multidimensional distribution of the power generator of pseudorandom numbers modulo a h...
For a real x ≥ 1 we denote by Sk[X] the set of k-full integers n ≤ x, that is, the set of positive i...
AbstractFor a real x ⩾-1 we denote by Sk[X] the set of k-full integers n ⩽ x, that is, the set of po...
AbstractLet p be a prime, u be a linear recurring sequence of integers of order d and let S=3d2+9d2+...
AbstractFor a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of ...
summary:A positive integer $n$ is called a square-free number if it is not divisible by a perfect sq...
An x-pseudopower to base g is a positive integer which is not a power of g yet is so modulo p for al...
Let g be a primitive root modulo a prime p. It is proved that the triples (gx, gy, gxy), x, yfl 1, …...
Let Fp be a prime field of p elements and let g be an element of Fp of multiplicative order t modulo...
Let g be a primitive root modulo a (n+1)-bit prime p. In this paper we prove the uniformity of distr...
http://www.math.missouri.edu/~bbanks/papers/index.htmlLet p be a prime and 79 an integer of order t ...
Abstract. Let p be a prime and V an integer of order t in the multiplicative group modulo p. In this...
AbstractFor a fixed integer s≥2, we estimate exponential sums with alternative power sums As(n)=∑i=0...
For a fixed integer s ≥ 1, we estimate exponential sums with harmonic sums [equation omitted for for...
Let m = pl be a product of two distinct primes p and l. We show that for almost all exponents e with...
We study the multidimensional distribution of the power generator of pseudorandom numbers modulo a h...
For a real x ≥ 1 we denote by Sk[X] the set of k-full integers n ≤ x, that is, the set of positive i...
AbstractFor a real x ⩾-1 we denote by Sk[X] the set of k-full integers n ⩽ x, that is, the set of po...
AbstractLet p be a prime, u be a linear recurring sequence of integers of order d and let S=3d2+9d2+...
AbstractFor a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of ...
summary:A positive integer $n$ is called a square-free number if it is not divisible by a perfect sq...
An x-pseudopower to base g is a positive integer which is not a power of g yet is so modulo p for al...