Related papers: Conditional Negation of The abc Conjecture
We consider the gravitational correction to the running of gauge coupling. Weak gravity conjecture implies that the gauge theories break down when the gravitational correction becomes greater than the contribution from gauge theories. This…
The abc conjecture is one of the most famous unsolved problems in number theory. The conjecture claims for each real $\epsilon > 0$ that there are only a finite number of coprime positive integer solutions to the equation $a+b = c$ with $c…
We show that Vojta's conjecture for some rational surfaces is related to the $abc$ conjecture. More specifically, we prove that Vojta's conjecture on these surfaces implies a special case of the $abc$ conjecture, while the $abc$ conjecture…
The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an…
We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.
In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.
In this paper we prove the WALA conjecture.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.
The two envelopes paradox is discussed. By calculating the conditional probability, we arrive at a conditional expectations which differs from existing results.
The Collatz and $abc$ conjectures, both well known and thoroughly studied, appear to be largely unrelated at first sight. We show that assuming the $abc$ conjecture true is helpful to improve the lower bound of integers initiating a…
We show explicitly, for different types of extremal black holes, that test fields satisfying the null energy condition at the event horizon cannot violate the weak cosmic censorship conjecture. This is done by checking, in each case, that…
We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…
It is possible to obtain a large Bayes Factor (BF) favoring the null hypothesis when both the null and alternative hypotheses have low likelihoods, and there are other hypotheses being ignored that are much more strongly supported by the…
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.
We prove a central limit theorem with aassumptions which are many weak than classical conditions
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.