相关论文: Degree 1 elements of the Selberg class
We show the Graceful Tree Conjecture holds.
We present a novel family of $C^1$ quadrilateral finite elements, which define global $C^1$ spaces over a general quadrilateral mesh with vertices of arbitrary valency. The elements extend the construction by (Brenner and Sung, J. Sci.…
We describe a plan how to prove an effective Siegel theorem (about the exceptional Dirichlet character). We give a brief outline in Section 0. We give a more detailed plan in Sections 1-5. The missing details (mostly routine elementary…
In this note by using elementary considerations, we settle Fr\"oberg's conjecture for a large number of cases, when all generators of ideals have the same degree.
In this paper, we define a special class of elements in the algebras obtained by the Cayley Dickson process, called l elements. We find conditions such that these elements to be invertible. These conditions can be very useful for finding…
Transcendental Brauer elements are notoriously difficult to compute. Work of Wittenberg, and later, Ieronymou, gives a method for computing 2-torsion transcendental classes on surfaces that have a genus 1 fibration with rational 2-torsion…
We prove an $\mathbb F_p$-Selberg integral formula of type $A_n$, in which the $\mathbb F_p$-Selberg integral is an element of the finite field $\mathbb F_p$ with odd prime number $p$ of elements. The formula is motivated by analogy between…
We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.
We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…
We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…
We give an a priori proof of the known presentations of (that is, completeness of families of relations for) the principal subspaces of all the standard A_1^(1)-modules. These presentations had been used by Capparelli, Lepowsky and Milas…
We prove an $\mathbb F_p$-Selberg integral formula, in which the $\mathbb F_p$-Selberg integral is an element of the finite field $\mathbb F_p$ with odd prime number $p$ of elements. The formula is motivated by analogy between…
We prove that the Hilbert property is satisfied by certain del Pezzo surfaces of degree one and Picard rank 1 over fields finitely generated over $\mathbb{Q}$. We generalize results of the first author on elliptic surfaces and employ…
The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kahler manifold. As a consequence we obtain several results on…
The algebras of the title are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, over a field of positive characteristic $p$, that are generated by an element of degree $1$ and an element of degree $p$, and satisfy…
In this paper, we prove the category of finite length modules for the $\mathbb{Z}_2$-orbifold $M(1)^+$ of the Heisenberg vertex operator algebra whose simple composition factors are $M(1)^\pm$ or $M(1,\lambda)$ for $\lambda \in…
A short proof to a recent theorem of Giambruno and Mishchenko is given in this note.
The present work consists of three parts. In the first one we determine the prototypes of separable Rosenthal compacta and we provide a classification theorem. The second part concerns an extension of a theorem of S. Todorcevic. The last…
In this paper we consider Deligne-Lusztig varieties and their analogues when the Frobenius endomorphism is replaced with conjugation by an element in a group, especially a regular semisimple or regular unipotent one. We calculate their…
This is an exposition of the homological classification of actions of surface groups on the plane, in every degree of smoothness.