Related papers: On a conjecture by Blocki-Zwonek
This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.
These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).
This is the completely revised version of math.AG/0101071.
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.
In this note, we show that a "Toy Conjecture" made by (Boyle, Ishai, Pass, Wootters, 2017) is false, and propose a new one. Our attack does not falsify the full ("non-toy") conjecture in that work, and it is our hope that this note will…
We confirm several conjectures of Guo, Jouhet and Zeng concerning the factors of alternative binomials sums.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
We prove inversion of adjunction on log canonicity.
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
This note presents an interesting counterexample to a basic covering problem.
In this paper, we prove a conjecture proposed by George Beck, which involves gap-free partitions and partitions with distinct parts.
A counter example to the main result has been communicated to the author by Matei Toma.
In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.
We disprove a conjecture of Simon for higher-order Szego theorems for orthogonal polynomials on the unit circle and propose a modified version of the conjecture.
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…
In this article, we give two different proofs of why the Collatz Conjecture is false.
We prove a conjecture of K. Marton, widely known as the polynomial Freiman--Ruzsa conjecture, in characteristic $2$. The argument extends to odd characteristic, with details to follow in a subsequent paper.
We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.
We give counterexamples for the modification on Malle's Conjecture given by T\"urkelli. T\"urkelli's modification on Malle's conjecture is inspired by an analogue of Malle's conjecture over a function field. As a consequence, our…