A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences.
A short proof of a known density result.
A short proof of a series evaluation in terms of harmonic numbers.
A simple construction of minimal asymptotic bases
A slow-growing sequence defined by an unusual recurrence.
A special class of triangular arrays.
A special prime divisor of the sequence: .
A spectral gap theorem in SU
We establish the spectral gap property for dense subgroups of SU, generated by finitely many elements with algebraic entries; this result was announced...
A structure theory for small sum subsets
A study of Eulerian numbers for permutations in the alternating group.
A study on the -adic integral representation on associated with Bernstein and Bernoulli polynomials.
A study on the -adic -integral representation on associated with the weighted -Bernstein and -Bernoulli polynomials.
A theorem concerning systems of residue classes.
A theorem of Cobham for non-primitive substitutions
A theorem of H. Steinhaus and -dense sets of positive integers
A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function
We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli relations,...
A two-dimensional univoque set
Let J ⊂ ℝ² be the set of couples (x,q) with q > 1 such that x has at least one representation of the form with integer coefficients satisfying , i ≥ 1. In this case we say that is an expansion of x in base q. Let U be the set of couples (x,q) ∈ J such that x has exactly one expansion in base q. In this paper we deduce some topological and combinatorial properties of the set U. We characterize the closure of U, and we determine its Hausdorff dimension. For (x,q) ∈ J, we also prove new properties...
A Unified Theory of Proportion
A Unified Theory of Proportion
A uniform version of Jarník's theorem