On the number of polynomials of bounded measure
On the number of prime divisors of a binomial coefficient.
On the number of prime divisors of the iterates of the Carmichael function.
On the number of prime divisors of the order of elliptic curves modulo p
On the number of prime factors of a finite arithmetical progression
On the number of prime factors of integers of the form ab + 1
On the number of prime factors of summands of partitions
We present various results on the number of prime factors of the parts of a partition of an integer. We study the parity of this number, the extremal orders and we prove a Hardy-Ramanujan type theorem. These results show that for almost all partitions of an integer the sequence of the parts satisfies similar arithmetic properties as the sequence of natural numbers.
On the Number of Primitive Lattice Points in Plane Domains.
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