On the number of primitive Pythagorean triangles
On the number of primitive λ-roots
On the number of rational points of Jacobians over finite fields
We prove lower and upper bounds for the class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in the proof are essentially those from the explicit asymptotic theory of global fields. We thus provide a concrete application of effective results from the asymptotic theory of global fields and their zeta functions.
On the number of rational squares at fixed distance from a fifth power
On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression
We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer in the form with prime numbers such that , under suitable hypothesis on for every integer .
On the number of representations of a positive integer by a binary quadratic form
On the number of representations of a positive integer by certain quadratic forms
For natural numbers a,b and positive integer n, let R(a,b;n) denote the number of representations of n in the form . Lomadze discovered a formula for R(6,0;n). Explicit formulas for R(1,5;n), R(2,4;n), R(3,3;n), R(4,2;n) and R(5,1;n) are determined in this paper by using the (p;k)-parametrization of theta functions due to Alaca, Alaca and Williams.
On the number of representations of an integer by a linear form.
On the number of representations of integers as the sum of k terms
On the number of representations of integers by quadratic forms in twelve variables.
On the number of representations of integers by some quadratic forms in ten variables.
On the number of representations of n by ax² + bxy + cy²
On the number of representations of n by ax²+by(y-1)/2, ax²+by(3y-1)/2 and ax(x-1)/2+by(3y-1)/2
On the number of representations of positive integers by a direct sum of binary quadratic forms with discriminant .
On the number of representations of positive integers by quadratic forms as the basis of the space .
On the number of representations of positive integers by the quadratic form .
On the number of semigroups of natural numbers.
On the number of sign changes in the remainder-term of the prime-ideal theorem
On the Number of S-Integral Solutions to Ym = f(x).
On the number of solutions of a congruence in GF[q,x]