Related papers: A note on Kronecker's approximation theorem
We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We derive a relative version of the slicing Bennequin inequalities for cobordant Legendrian knots, and review a few proofs of the result.
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
We give a new proof of a classical theorem on approximation of continuous functions on totally real sets
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…
We draw connections between the various conjectures which are included in G. R\'emond's generalized Lehmer problems. Specifically, we show that the degree one form of his conjecture for the multiplicative group is, in a sense, almost as…
This note is an addendum to the paper ''Mahler's method in several variables and finite automata''. It strengthens part (i) of Theorem 1.1 of the aforementioned paper.
We give a combinatorial proof of a formula giving the partial sums of the $k$-bonacci sequence as alternating sums of powers of two multiplied by binomial coefficients. As a corollary we obtain a formula for the $k$-bonacci numbers.
We give a counting based proof of the Graham Pollak Theorem
We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…
We present a short and self-contained proof of the choosability version of Brooks' theorem.
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
We discuss some aspects of the theory of subelliptic estimates.
A very simple but useful almost sure convergence theorem of probability is given.
This note is a commentary on the model-theoretic interpretation of Grothendieck's double limit characterization of weak relative compactness.
We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.
We prove a sharp quantitative version of Hales' isoperimetric honeycomb theorem by exploiting a quantitative isoperimetric inequality for polygons and an improved convergence theorem for planar bubble clusters. Further applications include…
The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces.
We prove some new results related to Tanaka's formula.