Related papers: On PPT Square Conjecture

We prove explicit bounds for the number of sums of consecutive prime squares below a given magnitude.

We give a conjectural presentation of the infinitely generated group PGL(2,Q) with an infinite list of relators.

We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.

We prove the validity of the strong version of the union of uniform closed balls conjecture, formulated in 2011 as [4, Conjecture 2.5], in the plane.

In this note we will review the most important results and questions related to Chern conjecture and isoparametric hypersurfaces, as well as their interactions and applications to various aspects in mathematics.

A quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms is proved. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux.

We propose a projective version of the celebrated Brauer's Height Zero Conjecture on characters of finite groups and prove it, among other cases, for $p$-solvable groups as well as for (some) quasi-simple groups.

The polynomial Fre\u{\i}man--Ruzsa conjecture is a fundamental open question in additive combinatorics. However, over the integers (or more generally $\mathbb{R}^d$ or $\mathbb{Z}^d$) the optimal formulation has not been fully pinned down.…

We give a proof of Willcocks's Conjecture, stating that if $p - q$ and $p + q$ are relatively prime, then there exists a Hamiltonian tour of a $(p, q)$-leaper on a square chessboard of side $2(p + q)$. The conjecture was formulated by T. H.…

We show that Kaplansky's unit conjecture is true, under the assumption that the underlying field is complex.

Motivated by the Saxl conjecture and the tensor square conjecture, which states that the tensor squares of certain irreducible representations of the symmetric group contain all irreducible representations, we study the tensor squares of…

We present a new conjecture for the $SU_q(N)$ Perk-Schultz models. This conjecture extends a conjecture presented in our article (Alcaraz FC and Stroganov YuG (2002) J. Phys. A vol. 35 pg. 6767-6787, and also in cond-mat/0204074).

We survey various results and conjectures concerning multiple polylogarithms and the multiple zeta function. Among the results, we announce our resolution of several conjectures on multiple zeta values. We also provide a new integral…

We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We translate the problem into a question about closed…

We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…

Legendre's Conjecture is one of the most elegant open problems in Number Theory, which states that there is a prime between consecutive two perfect squares. In this note, we prove the conjecture holds true and also discuss the related…

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.

We present the proofs of the conjectures mentioned in the paper published in the proceedings of the 2024 AAAI conference [1], and discovered by the decomposition methods presented in the same paper.

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.