Related papers: The prime geodesic theorem for higher rank spaces

Let $\Gamma=PSL(2,Z[i])$ be the Picard group and $H^3$ be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient $\Gamma \setminus H^3$, called the Picard manifold, obtaining an error term of size…

Based on the Gale-Ryser theorem for the existence of suitable $(0,1)$-matrices for different partitions of a natural number, we revisit the classical result of G. G. Lorentz regarding the characterization of a plane measurable set, in terms…

An effective algorithm of determining Gromov--Witten invariants of smooth hypersurfaces in any genus (subject to a degree bound) from Gromov--Witten invariants of the ambient space is proposed. The Appendix is joint with E. Schulte-Geers.

This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "`a la Bott" for arithmetic…

In this paper we study fundamental properties of geodesic mappings with respect to the smoothness class of metrics. We show that geodesic mappings preserve the smoothness class of metrics. We study geodesic mappings of Einstein spaces.

The study of the Lefschetz properties of Artinian graded algebras was motivated by the hard Lefschetz theorem for a smooth complex projective variety, a breakthrough in algebraic topology and geometry. Over the last few years, this topic…

We provide a simpler proof of the hard Lefschetz Theorem for face rings of PL spheres: While the algebraic theory remains the same, we replace the geometric constructions by Pachner's Theorem. This simplifies the reasoning for an important…

In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…

Consider a Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem…

The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in…

We show that a trivial case of Janelidze's categorical Galois theorem can be used as a key step in the proof of Joyal and Tierney's result on the representation of Grothendieck toposes as localic groupoids. We also show that this trivial…

We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…

We prove that the set of bounded geodesics in Teichmuller space are a winning set for Schmidt's game. This is a notion of largeness in a metric space that can apply to measure 0 and meager sets. We prove analogous closely related results on…

We obtain an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness…

Let $(E)$ a homogeneous linear differential equation of order $n$ Fuchsien over $\mathbb{P}^{1}(\mathbb{C}) $. The idea of Riemann (1857) was to obtain the properties of solutions of (E) by studying the local system. Thus, he obtained some…

In this paper we investigate possible extensions of the idea of geodesic completeness in complex manifolds, following two directions: metrics are somewhere allowed not to be of maximum rank, or to have 'poles' somewhere else. Geodesics are…

For a projective $2n$-dimensional irreducible holomorphic symplectic manifold $Y$ of generalized Kummer deformation type and $j$ the smallest prime number dividing $n+1$, we prove the Lefschetz standard conjectures in degrees…

In this article, we discuss the Lefschetz trace formula for an adic space which is separated smooth of finite type but not necessarily proper over an algebraically closed non-archimedean field. Under a certain condition on the absence of…

We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the…

Two well known facts from elementary number theory are proven by using Bergman spaces.