On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree
On the number of ideals free from large prime divisors.
On the number of integers n such that nd(n) ≤ x
On the number of integers represented by systems of Abelian norm forms
On the number of integers which are sums of two squares
On the Number of Integral Ideals in Galois Extensions.
On the number of irreducible factors of a polynomial II
On the number of irreducible polynomials with 0,1 coefficients
On the number of large integer points on elliptic curves
On the number of lattice points in certain planar segments
On the number of lattice points inside a closed curve
On the number of m-term zero-sum subsequences
On the number of nonquadratic residues which are not primitive roots
We show that there exist infinitely many positive integers r not of the form (p-1)/2 - ϕ(p-1), thus providing an affirmative answer to a question of Neville Robbins.
On the number of orthogonal systems in vector spaces over finite fields.
On the number of pairs of binary forms with given degree and given resultant
On the number of pairs of partitions of n without common subsums
On the Number of Partitions of an Integer in the -bonacci Base
For each we consider the -bonacci numbers defined by for and for When these are the usual Fibonacci numbers. Every positive integer may be expressed as a sum of distinct -bonacci numbers in one or more different ways. Let be the number of partitions of as a sum of distinct -bonacci numbers. Using a theorem of Fine and Wilf, we obtain a formula for involving sums of binomial coefficients modulo In addition we show that this formula may be used to determine the number of partitions...
On the number of perfect binary quadratic forms.
On the number of places of convergence for Newton’s method over number fields
Let be a polynomial of degree at least 2 with coefficients in a number field , let be a sufficiently general element of , and let be a root of . We give precise conditions under which Newton iteration, started at the point , converges -adically to the root for infinitely many places of . As a corollary we show that if is irreducible over of degree at least 3, then Newton iteration converges -adically to any given root of for infinitely many places . We also conjecture that...
On the number of points on abelian and Jacobian varieties over finite fields
We give upper and lower bounds for the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces.