Related papers: On three conjectures of P. Barry
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
The conjectures of Manin and Peyre are confirmed for a certain threefold.
In terms of Sear's transformation formula for $_4\phi_3$-series, we give new proofs of a summation formula for ${_4\phi_3}$-series due to Andrews [2] and another summation formula for${_4\phi_3}$-series conjectured in the same paper.…
We prove Poincare's Conjecture that every simply connected, closed three-manifold is topologically equivalent to the three-sphere. The proof is founded on the algebraic formulation discovered by J. Stallings.
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
We prove a conjecture due to Y. Last on Jacobi matrices.
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.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We reprove a few results concerning paperfolding sequences using properties of Catalan numbers modulo 2.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
We provide a broad class of counterexamples to a conjecture of L. de Branges concerning the superfluity of the continuity property in the axiomatic description of de Branges spaces.
We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.
The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.
The paper presents a counterexample to the Hodge conjecture.
In the recent article arXiv:1606.03351, Apagodu and Zeilberger discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the end they…
In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
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)