Counting Keith numbers.
Counting Maximal Distance-Independent Sets in Grid Graphs
Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied
Counting monic irreducible polynomials in for which order of is odd
Hasse showed the existence and computed the Dirichlet density of the set of primes for which the order of is odd; it is . Here we mimic successfully Hasse’s method to compute the density of monic irreducibles in for which the order of is odd. But on the way, we are also led to a new and elementary proof of these densities. More observations are made, and averages are considered, in particular, an average of the ’s as varies through all rational primes.
Counting non-isomorphic maximal independent sets of the -cycle graph.
Counting optimal joint digit expansions.
Counting -groups and nilpotent groups
Counting pattern-free set partitions. II: Noncrossing and other hypergraphs.
Counting periodic points of -adic power series
Counting points in medium characteristic using Kedlaya's algorithm.
Counting points of fixed degree and bounded height
Counting points on elliptic curves over finite fields
We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic polynomial...
Counting problems and semisimple groups.
Counting rational points near planar curves
We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → ℝ is a sufficiently smooth function defined on the interval [η,ξ], then the number of rational points with denominator no larger than Q that lie within a δ-neighborhood of the graph of f is shown to be asymptotically equivalent to (ξ-η)δQ².
Counting rational points on a certain exponential-algebraic surface
We study the distribution of rational points on a certain exponential-algebraic surface and we prove, for this surface, a conjecture of A. J. Wilkie.
Counting rational points on cubic and quartic surfaces
Counting rational points on del Pezzo surfaces with a conic bundle structure
For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.
Counting rational points on hypersurfaces of low dimension
Counting solutions of decomposable form equations
Counting with Gauss' sums.
Coupling of universal monodromy representations of Galois-Teichmüller modular groups.