Related papers: A Remark on the Higher Capelli Identities
In this paper, we propose a generalization of a congruence due to Carlitz.
The topological index of a surface was previously introduced by the first author as the topological analogue of the index of an unstable minimal surface. Here we show that surfaces of arbitrarily high topological index exist.
We consider the task of upscaling a low resolution thumbnail image of a person, to a higher resolution image, which preserves the person's identity and other attributes. Since the thumbnail image is of low resolution, many higher resolution…
In this note, we prove some combinatorial identities and obtain a simple form of the eigenvalues of $q$-Kneser graphs.
We define the height of a mixed motive over a number field extending our previous work for pure motives.
We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.
In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have…
We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.
We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the corresponding Jacobian. The method used in the proof is a…
In this paper, another proof of Pell identities is presented by using the determinant of tridiagonal matrices. It is calculated via the Laplace expansion.
Jacobi's triple product identity is proved from one of Euler's $q$-exponential functions in an elementary way.
We introduce the discrete hierarchy which naturally generalizes well known discrete KP hierarchy.
We claim to resolve the P=?NP problem via a formal argument for P=NP.
We present a simple proof and a generalization of a Menon-type identity by Li, Hu and Kim, involving Dirichlet characters and additive characters.
In this paper we prove the existence of all higher logarithms as multivalued and ordinary Deligne cohomology classes.
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We give an accessible and modern description of the automorphisms of a finite abelian group $G$. Included is an explicit formula for the cardinality of $Aut(G)$.
In this note, we give a slight improvement of a result of A. K\"uronya and V. Lozovanu about higher syzygies on abelian surfaces.
The abstract will be added in due course.