Related papers: On some conjectures by Lu and Wenzel
In this paper, using quaternion arithmetic in the ring of Lipschitz integers, we present a proof of Zh\`i-W\v{e}i S\={u}n's "1-3-5 conjecture" for integral solutions, and for all natural numbers greater than a specific constant. This,…
We show that the Friedlander-Mazur conjecture holds for a complex smooth projective variety X of dimension three implies the standard conjectures hold for X. This together with a result of Friedlander yields the equivalence of the two…
In this note we apply the billiard technique to deduce some results on Viterbo's conjectured inequality between volume of a convex body and its symplectic capacity. We show that the product of a permutohedron and a simplex (properly related…
We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…
We formulate Vojta's conjecture for smooth weighted projective varieties, weighted multiplier ideal sheaves, and weighted log pairs and prove that all three versions of the conjecture are equivalent. In the process, we introduce generalized…
It was conjectured that the augmentation ideal of a dihedral quandle of even order $n>2$ satisfies $|\Delta^k(\text{R}_n)/\Delta^{k+1}(\text{R}_{n})|=n$ for all $k\geq 2$. In this article we provide a counterexample against this conjecture.
At the end of 1960's, Lawrence Zalcman posed a conjecture that the coefficients of univalent functions $f(z) = z + \sum\limits_2^\infty a_n z^n$ on the unit disk satisfy the sharp inequality $|a_n^2 - a_{2n-1}| \le (n-1)^2$, with equality…
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.
In this paper, we will introduce an extension to the Collatz's conjecture. This conjecture may be seen as a general conjecture that unifies the Collatz one together with many other similar conjectures. For instance, we propose our new…
We upgrade Howard's divisibility toward Perrin-Riou's Heegner point Main Conjecture to an equality under some mild conditions. We do this by exploiting Wei Zhang's proof of the Kolyvagin conjecture. The main ingredient is an improvement of…
We show that a weak form of the generalized Bocherer's conjecture implies multiplicity one for Siegel cusp forms of degree 2.
Friedlander and Mazur proposed a conjecture of hard Lefschetz type on Lawson homology. We shall relate this conjecture to Suslin conjecture on Lawson homology. For abelian varieties, this conjecture is shown to be equivalent to a vanishing…
In this paper we prove three power-exponential inequalities for positive real numbers. In particular, we conclude that this proofs give affirmatively answers to three, until now, open problems (conjectures~4.4, 2.1 and 2.2) posed by…
This paper presents some new inequalities, the most important of which is the inequality given in Theorem 2.1. It can solve a class of inequalities by a unified method. An important application of the inequality given in Theorem 2.1 is to…
The new type of "bumping" of the Muckenhoupt $A_2$ condition on weights is introduced. It is based on bumping the entropy integral of the weights. In particular, one gets (assuming mild regularity conditions on the corresponding Young…
The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of…
The BK inequality (\cite{BK85}) says that,for product measures on $\{0,1\}^n$, the probability that two increasing events $A$ and $B$ `occur disjointly' is at most the product of the two individual probabilities. The conjecture in…
I. M. Milin proposed, in his 1971 paper, a system of inequalities for the logarithmic coefficients of normalized univalent functions on the unit disk of the complex plane. This is known as the Lebedev-Milin conjecture and implies the…
In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…
Andrews, Dixit, Schultz, and Yee conjecture the parity of a double Lambert series. In 2026, Amdeberhan, Andrews, and Ballantine offer some ideas that are pointing in the right direction for the proof. In this paper, we complete the rest of…