相关论文: The Strong Macdonald Conjecture

We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly log-concavity on $\mathbb{R}$ under convolution follows from…

In the paper a theorem of Piccard's type is proved and, consequently, the continuity of $\mathcal{D}$-measurable polynomial functions of $n$-th order as well as $\mathcal{D}$-measurable $n$-convex functions is shown. The paper refers to the…

We characterize all the strongly monotypic polytopes. Hadwiger's conjecture for this class of polytopes is deduced from the characterization.

A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…

The article provides a counterexample to a conjecture by Blocki-Zwonek.

In this paper, we prove the Farrell-Jones Conjecture for the solvable Baumslag-Solitar groups with coefficients in an additive category. We also extend our results to groups of the form, Z[1/p] semidirect product with any virtually cyclic…

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 paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

Expansions of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N} ; < \rangle$ have been a fertile and active area of research ever since the publication of the seminal papers of B\"uchi and Elgot & Rabin on the…

The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson theorem or the $q$-Dyson constant term identity. This conjecture was proved by K\'{a}rolyi, Lascoux and Warnaar…

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

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

We survey the history of Shelah's conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that the conjecture implies that every strongly dependent field…

We study the equivariant local epsilon constant conjecture, denoted by $C_{EP}^{na}(N/K,V)$, as formulated in various forms by Kato, Benois and Berger, Fukaya and Kato and others, for certain 1-dimensional twists…

Real-stable, Lorentzian, and log-concave polynomials are well-studied classes of polynomials, and have been powerful tools in resolving several conjectures. We show that the problems of deciding whether a polynomial of fixed degree is real…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…

We state and prove a new closure theorem closely related to the classical closure theorems of Poncelet and Steiner. Along the way, we establish a number of theorems concerning conic sections.