On the number of subgroups of given index in the modular group.
On the number of subsets of relatively prime to and asymptotic estimates.
On the number of subsets relatively prime to an integer.
On the number of sums and products
On the number of terms of a composite polynomial
On the number of terms of a power of a polynomial
On the number of values taken by a polynomial over a finite field
On the number of ways of writing as a product of factorials.
On the number of y-smooth natural numbers ... representable as a sum of two integer squares.
On the number of zero trace elements in polynomial bases for F2n.
Let Fq denote the finite field of q elements. O. Ahmadi and A. Menezes have recently considered the question about the possible number of elements with zero trace in polynomial bases of F2n over F2. Here we show that the Weil bound implies that there is such a basis with n + O(log n) zero-trace elements.
On the numbers of solutions of weighted unit equations
On the numbers that are representable as the sum of two cubes.
On the number-theoretic functions ν(n) and Ω(n)
On the odd part of tame kernels of biquadratic number fields
On the Oesterlé-Masser Conjecture.
On the Olson and the Strong Davenport constants
A subset of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, -groups with large rank relative to the exponent, including all groups with exponent at most five. These results are derived as consequences of more general...
On the one-sided boundedness of discrepancy function of the sequence {nα}
On the orbits of Singer groups and their subgroups.
On the order function of a transcendental number
On the order of Dedekind Zeta-functions near the line σ = 1