Inhomogeneous diophantine approximation on polynomials in
Inhomogeneous extreme forms
G.F. Voronoi (1868–1908) wrote two memoirs in which he describes two reduction theories for lattices, well-suited for sphere packing and covering problems. In his first memoir a characterization of locally most economic packings is given, but a corresponding result for coverings has been missing. In this paper we bridge the two classical memoirs.By looking at the covering problem from a different perspective, we discover the missing analogue. Instead of trying to find lattices giving economical...
Inhomogeneous Minimum of Indefinite Quadratic Forms in Five Variables of Type (3, 2) or (2, 3): A Conjecture of Watson.
Inhomogeneous norm form equations over function fields
Initial layers of -extensions of complex quadratic fields
Initial powers of Sturmian sequences
Injectivity properties of liftings associated to weil representations
Inmersiones de órdenes cuadráticos en el orden generador por T^iN).
Integer matrices related to Liouville's function
In this note, we construct some integer matrices with determinant equal to certain summation form of Liouville's function. Hence, it offers a possible alternative way to explore the Prime Number Theorem by means of inequalities related to matrices, provided a better estimate on the relation between the determinant of a matrix and other information such as its eigenvalues is known. Besides, we also provide some comparisons on the estimate of the lower bound of the smallest singular value. Such discussion...
Integer partitions and convexity.
Integer partitions into arithmetic progressions with an odd common difference.
Integer partitions, tilings of -gons and lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a -gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer Partitions, Tilings of 2D-gons and Lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer partitions with fixed subsums.
Integer Points and the Rank of Thue Elliptic Curves.
Integer Points Close to a Smooth Curve
∗ This research is partially supported by the Bulgarian National Science Fund under contract MM-403/9We review the existing estimates for the number of integer points close to a smooth curve and improve on some of these.
Integer points close to convex hypersurfaces
Integer points close to convex surfaces
Integer Points on Curves and Surfaces.
Integer points on curves of genus 1