相关论文: Notes on the Milnor conjectures

New cases of the multiplicity conjecture are considered.

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

We sketch several proofs of F\'ary--Milnor theorem.

In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

These notes contain an introduction to proofs of Farrell-Jones Conjecture for some groups and are based on talks given in Ohio, Oxford, Berlin, Shanghai, M\"unster and Oberwolfach in 2011 and 2012.

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

In this paper we prove the 2-local part of the Beilinson-Lichtenbaum conjectures on tosion in motivic cohomology. In particular we prove the Milnor conjecture relating Milnor's K-theory and the Galois cohomology with Z/2-coefficients. This…

In a recent talk of Robbert Fokkink, some conjectures related to the infinite Tribonacci word were stated by the speaker and the audience. In this note we show how to prove (or disprove) the claims easily in a "purely mechanical" fashion,…

We obtain simple proofs of certain inequalites for bivariate means.

A proof of Sendov's conjecture is given.

In this paper we propose generalizations of the Sokolov-Ternov and Unruh effects, and discuss the possibility to measure them on different experiments.