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
On the order of lacunary sums of binomial coefficients.
On the order of magnitude of the difference between consecutive prime numbers
On the order of points on curves over finite fields.
On the order of the Mertens function.
On the order of unimodular matrices modulo integers
On the order of vanishing of modular -functions at the critical point
On the order of
On the order three Brauer classes for cubic surfaces
We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over ℚ such that Br(S)/Br(ℚ) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.