Related papers: Notes on the Milnor conjectures
Analogues of Kolmogorov comparison theorems and some of their applications were established.
The aim of this short note is to provide a proof to a statement of Sierpi\'nski concerning the number of possible sums of a series (of type $\lambda<\aleph_1$) of arbitrary ordinal numbers.
In this paper we prove the validity of a formula for computing the Alexander invariant which was originally conjectured by Bar-Natan and Dancso in [BND].
In this paper, we obtain new results on the critical points of a polynomial, these results are useful to the Sendov conjecture.
The purpose of this note is to show by constructing counterexamples that two conjectures of M\'{o}ri and Sz\'{e}kely for the Borel-Cantelli lemma are false.
This note (originally from 2015) provides a proof of a 1985 conjecture of Montiel and Ros concerning the conformal volume of tori. This updated version adds a proof of the claim made in Remark 5 about the value of the conformal volume of…
In this article, we prove the conjecture of Bar-Natan, Garoufalidis, and Khovanov's on the support of the Khovanov's invariants for alternating knots.
This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
In this note I respond to Vilenkin's claim that there must have been a beginning.
We prove a conjecture by W. Bergweiler and A. Eremenko on the traces of elements of modular group in this paper
We survey the classical results on the prime number theorem
In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.
We show that the Conjecture of Voevodsky concerning slices of the algebraic cobordism spectrum MGL implies a general statement about the slices of motivic Landweber spectra. In particular it confirms the possible approach suggested by…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
In this paper, we obtain new results on the critical points of a polynomial. We discuss the Sendov conjecture for polynomials of degree nine.
In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.
Six conjectures on pairs of consecutive primes are listed in this paper, together with examples for each case.
The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.
First, we shall formulate and prove Theorem of Lie-Kolchin type for a cone and derive some algebro-geometric consequences. Next, inspired by a recent result of Dinh and Sibony we pose a conjecture of Tits type for a group of automorphisms…