Related papers: An explicit prime geodesic theorem for discrete to…

In this short note we prove a version of Bertini's theorem for unipotent rigid fundamental groups, stating that for every smooth, projective, geometrically connected variety $X$ over an infinite perfect field $k$ of characteristic $p>0$,…

We compute the group homology, the topological K-theory of the reduced C^*-algebra, the algebraic K-theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4.…

Let $n\ge2$ and $\Omega$ be a bounded non-tangentially accessible domain (for short, NTA domain) of $\mathbb{R}^n$. Assume that $L_D$ is a second-order divergence form elliptic operator having real-valued, bounded, measurable coefficients…

The generating functions of the Severi degrees for sufficiently ample line bundles on algebraic surfaces are multiplicative in the topological invariants of the surface and the line bundle. Recently new proofs of this fact were given for…

We compute the automorphism groups of the Torelli complex and the complex of separating curves for all but finitely many compact orientable surfaces. As an application, we show that the abstract commensurators of the Torelli group and the…

In this paper we study local-global principles for tori over semi-global fields, which are one variable function fields over complete discretely valued fields. In particular, we show that for principal homogeneous spaces for tori over the…

We present an explicit formula for the discrete power function introduced by Bobenko, which is expressed in terms of the hypergeometric \tau functions for the sixth Painlev\'e equation. The original definition of the discrete power function…

In this work we investigate the heat kernel of the Laplace--Beltrami operator on a rectangular torus and the according temperature distribution. We compute the minimum and the maximum of the temperature on rectangular tori of fixed area by…

A recent paper of Church, Ellenberg, and Farb uses topology and representation theory of the symmetric group to prove enumerative results about square-free polynomials and F-stable maximal tori of the general linear group over the algebraic…

The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics of eigenvalues in the bulk of spectrum near a Fisher-Hartwig…

The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Jacobi-Sobolev bilinear form with mass point at $-1$ and/or $+1$. In particular, we construct the orthogonal polynomials using…

Consider a simple algebraic group $G$ of classical type and its Lie algebra $\mathfrak{g}$. Let $(e,h,f) \subset \mathfrak{g}$ be an $\mathfrak{sl}_2$-triple and $Q_e= C_G(e,h,f)$. The torus $T_e$ that comes from the…

A Richelot isogeny between Jacobian varieties is an isogeny whose kernel is included in the $2$-torsion subgroup of the domain. A Richelot isogeny whose codomain is the product of two or more principally polarized abelian varieties is…

We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…

We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…

In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of $TT^*Q$…

Algebraic surfaces of general type with $q=0$, $p_g=2$ and $K^2=1$ were described by Enriques and then studied in more detail by Horikawa. In this paper we consider a $16$-dimensional family of special Horikawa surfaces which are certain…

Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…

We study the distribution of closed geodesics for the modular surface. We improve the error term in the prime geodesic theorem, and obtain results on prime geodesics in very short intervals conditionally on the generalized Riemann…

We consider the Laplacian associated with a general metric in the canonical conformal structure of the noncommutative two torus, and calculate a local expression for the term a_4 that appears in its corresponding small-time heat kernel…