Related papers: Summary on the proof of BAB Conjecture

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

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

Several results about the union-closed sets conjecture are presented.

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

In this paper we give an outline on the Bayesian Decision Theory.

We present a proof of a combinatorial conjecture from the second author's Ph.D. thesis. The proof relies on binomial and multinomial sums identities. We also discuss the relevance of the conjecture in the context of PAC-Bayesian machine…

An overview of last seven years results concerning Sarnak's conjecture on M\"obius disjointness is presented, focusing on ergodic theory aspects of the conjecture.

In this paper we consider the remaining cases of Hebey-Vaugon conjecture.

This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

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

This is an introductory article to the theory of multiple gaps.

We provide a proof of the Borwein Conjecture using analytic methods.

In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.