Related papers: A proof of Sendov's conjecture
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
We prove inversion of adjunction on log canonicity.
We discuss the validity of the proof of the fixed numerator conjecture on Markov numbers, which is the main result of the paper mentioned in the title.
In this paper we present a complete proof of a conjecture due to V. V. Prelov in 2010 about an information inequality for the binary entropy function.
A conjecture of Sendov states that if a polynomial has all its roots in the unit disk and if $\beta$ is one of those roots, then within one unit of $\beta$ lies a root of the polynomial's derivative. If we define $r(\beta)$ to be the…
This is an exposition of Gauss's proof of Descartes's rule of signs.
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].
We provide a simple proof of Kamp's theorem.
We prove the geometric Bogomolov conjecture over a function field of characteristic zero.
Based on the recent work of Arsovski, we confirm a conjecture of Feng, Sun, and Xiang, and we give a shortened proof of Snevily's conjecture.
In this note, we disprove two Romanov type conjectures posed by Chen.
We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)
We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture.
We prove several extensions of the Erdos-Fuchs theorem.
Written for the book "Mathematicians from Saint Petersburg and their theorems".
We prove a result on the existence of linear forms of a given Diophantine type.