Related papers: Counterexamples to Okounkov's Log-Concavity Conjec…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We show that the sequence of moments of order less than 1 of averages of i.i.d. positive random variables is log-concave. For moments of order at least 1, we conjecture that the sequence is log-convex and show that this holds eventually for…

In this paper, we develop the theory of relative log convergent cohomology of radius $\lambda$ ($0 < \lambda \leq 1$), which is a generalization of the notion of relative log convergent cohomology in the previous paper. By comparing this…

In this note, we discuss recently discovered counterexamples to Mordell's Pellian Equation Conjecture and the Ankeny-Artin-Chowla-Conjecture. We provide a verification of the counterexample to Mordell's Pellian Equation Conjecture that can…

We provide a counterexample to P.~Olver's freeness conjecture for $C^\omega$ transformations.

We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We prove the ACC conjecture for local volumes. Moreover, when the local volume is bounded away from zero, we prove Shokurov's ACC conjecture for minimal log discrepancies.

In this paper, we prove the generic overconvergence of relative rigid cohomology with coefficient, by using the semistable reduction conjecture for overconvergent $F$-isocrystals (which is recently shown by Kedlaya).

The original version of the paper claimed to disprove the pseudo-Riemannian Lichnerowicz conjecture of D'Ambra and Gromov. However, the argument contains a crucial sign error in the lines following equation (8).

Khabibullin's conjecture has three statements equivalent to each other. Recently Ruslan Sharipov has constructed a counterexample to this conjecture for one of its three statements. In this paper Sharipov's counterexample is transferred to…

We give simple new proofs of two well-known results for the Schr\"odinger operator: first, the Brunn--Minkowski inequality for Dirichlet eigenvalues and, second, the log-concavity of the first Dirichlet eigenfunction. Our proof of the first…

In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…

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

We prove the reverse ultra log-concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-concavity of the sequence $\{i!d_i(m)\}$ for any $m\geq 2$, where $d_i(m)$ are the coefficients of the…

We give a new geometric proof of a conjecture of Fulton on the Littlewood-Richardson coefficients. This conjecture was firstly proved by Knutson, Tao and Woodward using the Honeycomb theory. A geometric proof was given by Belkale. Our proof…

A ``self--similar'' example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.

We disprove a recent conjecture regarding discrete distributions and their generating polynomials stating that strong log-concavity implies log-submodularity.

By inventing the notion of honeycombs, A. Knutson and T. Tao proved the saturation conjecture for Littlewood-Richardson coefficients. The Newell-Littlewood numbers are a generalization of the Littlewood-Richardson coefficients. By…