Primes in Arithmetic Progressions to Large Moduli. II.
Primitive Points on a Modular Hyperbola
For positive integers m, U and V, we obtain an asymptotic formula for the number of integer points (u,v) ∈ [1,U] × [1,V] which belong to the modular hyperbola uv ≡ 1 (mod m) and also have gcd(u,v) =1, which are also known as primitive points. Such points have a nice geometric interpretation as points on the modular hyperbola which are "visible" from the origin.
Primitive roots and powers among values of polynomials over finite fields.
Pseudorandom sequences of binary vectors
Quelques remarques sur les sommes exponentielles
Remarks on the upper bound for L(1,χ)
Short character sums with Fermat quotients
Some aspects of Davenport's work
Some mean-value theorems for exponential sums
Some new sums related to D. H. Lehmer problem
About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let be a prime, and let denote the number of all such that and
Sommes d’exponentielles dans
Sums of Kloosterman Sums.
Ternary quadratic forms with rational zeros
We consider the Legendre quadratic formsand, in particular, a question posed by J–P. Serre, to count the number of pairs of integers , for which the form has a non-trivial rational zero. Under certain mild conditions on the integers , we are able to find the asymptotic formula for the number of such forms.
The distribution of square-free numbers
The divisor function in arithmetic progressions
The equation n₁n₂ = n₃n₄, the gcd-sum function and the mean values of certain character sums
The first moment of quadratic Dirichlet L-functions
The -invariance of the Potts Hamiltonian.
The growth rate of the Dedekind Zeta-function on the critical line
The least primitive root in number fields