相关论文: Height zeta functions of toric bundles over flag v…
We investigate analytic properties of height zeta functions of toric varieties. Using the height zeta functions, we prove an asymptotic formula for the number of rational points of bounded height with respect to an arbitrary line bundle…
We study analytic properties of height zeta functions of equivariant compactifications of the Heisenberg group.
In this brief note, we will investigate the number of points of bounded (twisted) height in a projective variety defined over a function field, where the function field comes from a projective variety of dimension greater than or equal to…
For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on…
We introduce a new approach to study height zeta functions of projective spaces and projective bundles. To study height zeta functions of projective spaces $Z(\mathbb{P}^n, H_{\mathcal{O}(1)}; s)$, we apply the Riemann-Roch theorem of…
Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated…
We investigate the analytic properties of the zeta-function associated with heights on equivariant compactifications of anisotropic tori over number fields. This allows to verify conjectures about the distribution of rational points of…
We compute the equivariant zeta function for bundles over infinite graphs and for infinite covers. In particular, we give a ``transfer formula'' for the zeta function of infinite graph covers. Also, when the infinite cover is given as a…
We study topological zeta functions of complex plane curve singularities using toric modifications and further developments. As applications of the research method, we prove that the topological zeta function is a topological invariant for…
We define various height functions for motives over number fields. We compare these height functions with classical height functions on algebraic varieties, and also with analogous height functions for variations of Hodge structures on…
We investigate the anticanonical height zeta function of a (non necessarily split) toric variety defined over a global field of positive characteristic, drawing our inspiration from the method used by Batyrev and Tschinkel to deal with the…
The aim of this paper is to apply the work of Morris on Eisenstein series over global function fields to the study of the asymptotic behavior of the points of bounded height on a generalized flag variety defined as the quotient of a…
We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov…
We introduce new non-abelian zeta functions for curves defined over finite fields. There are two types, i.e., pure non-abelian zetas defined using semi-stable bundles, and group zetas defined for pairs consisting of (reductive group,…
In the present manuscript, we study analytic properties of zeta functions defined by partial Euler products.
We study the Selberg zeta and the theta function associated to bundles over even-dimensional locally symmetric spaces of rank one.
In this paper, we give concrete descriptions of leafwise cohomology groups and show the regularized determinant expression of the dynamical zeta function for fiber bundles over $S^{1}$. As applications, we show a functional equation and…
The theory of Selberg zeta functions is generalized to higher rank spaces. Applications towards analytic torsion numbers are given.
We apply the theory of height zeta functions to study the asymptotic distribution of rational points of bounded height on projective equivariant compactifications of semi-direct products.
The higher rank Lefschetz formula for p-adic groups is used to prove rationality of a several-variable zeta function attached to the action of a p-adic group on its Bruhat-Tits building. By specializing to certain lines one gets…