The cyclotomic numbers of order twenty
The -dimensional Gauss transformation: Strong convergence and Lyapunov exponents.
The D(1)-extensions of D(-1)-triples 1,2,c and integer points on the attached elliptic curves
The Davenport constant of a box
Given an additively written abelian group G and a set X ⊆ G, we let (X) denote the monoid of zero-sum sequences over X and (X) the Davenport constant of (X), namely the supremum of the positive integers n for which there exists a sequence x₁⋯xₙ in (X) such that for each non-empty proper subset I of 1,...,n. In this paper, we mainly investigate the case when G is a power of ℤ and X is a box (i.e., a product of intervals of G). Some mixed sets (e.g., the product of a group by a box) are studied...
The decomposition of
The defect of weak approximation for homogeneous spaces
The degree of the splitting field of a random polynomial over a finite field.
The densest lattice in twenty-four dimensions.
The density of integral points on hypersurfaces of degree at least four
The density of rational and integral points on algebraic varieties
The density of rational points on a pfaff curve
This paper is concerned with the density of rational points on the graph of a non-algebraic pfaffian function.
The density of rational points on cubic surfaces
The density of representation degrees
For a group and a positive real number , define to be the number of integers less than which are dimensions of irreducible complex representations of . We study the asymptotics of for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups in characteristic zero, showing that either there exists such that for all large , or is virtually abelian (in which case is bounded).
The density of S-integral points in projective space with respect to a quadric
The density of the set of sums
The derivative of p-adic L-functions
The determinant of the Laplacian on the n-sphere
The determination of all four-digit Kaprekar constants.
The determination of parabolic points in modular and extended modular groups by continued fractions.
The Deuring-Safarevic Formula Revisited.