Related papers: On the WALA conjecture, Alberti representations an…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We provide a proof of the Borwein Conjecture using analytic methods.
The paper presents a counterexample to the Hodge conjecture.
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.
Recently, Wang and Ma propose a conjecture associated with the possible generalization of Andrews-Warnaar identities. It is confirmed in this paper. As the applications of this conjecture, we prove that a family of series can be expressed…
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
This memoire consists of two main results. In the first one we describe Ricci flow theory and we give an educative way for proving Elliptization Conjecture and then we prove Poincare conjecture which is the second proof of Perelman for…
We prove some new results related to Tanaka's formula.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
In this paper, we apply high level versions of Jacobi's derivative formula to number theory such as quarternary quadratic forms and convolution sums of some arithmetical functions.
A proof is given of Rosenthal's \(\ell_1\) theorem.
We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.
We prove a conjecture due to Y. Last on Jacobi matrices.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
We show the existence of a large family of representations supported by the orbit closure of the determinant. However, the validity of our result is based on the validity of the celebrated `Latin Square Conjecture' due to Alon-Tarsi or more…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
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].
The subject of this paper is a simulation to that in [1] but here we consider substitutions corresponding to transpositions instead of replacements.