Related papers: Rational Points of Bounded Height on Compactificat…
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.
We study analytic properties of height zeta functions of equivariant compactifications of the Heisenberg group.
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 prove Manin's conjecture concerning the distribution of rational points of bounded height, and its refinement by Peyre, for wonderful compactifications of semi-simple algebraic groups over number fields. The proof proceeds via the study…
We prove asymptotic formulas for the number of rational points of bounded height on smooth equivariant compactifications of the affine space. (Nous \'etablissons un d\'eveloppement asymptotique du nombre de points rationnels de hauteur…
We prove asymptotic formulas for the number of rational points of bounded height on certain equivariant compactifications of the affine plane.
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…
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…
We study the distribution of rational points of bounded height on a one-sided equivariant compactification of $\mathrm{PGL}_2$ using automorphic representation theory of $\mathrm{PGL}_2$.
We prove asymptotic formulas for the number of rational points of bounded height on certain blow-ups of the projective space.
We study the asymptotic distribution of S-integral points of bounded height on partial bi-equivariant compactifications of semi-simple groups of adjoint type.
We investigate analytic properties of height zeta functions of toric bundles over flag varieties.
We prove Manin's conjecture for bi-equivariant compactifications of unipotent groups.
We study the asymptotic distribution of integral points of bounded height on partial bi-equivariant compactifications of semi-simple groups of adjoint type.
We study the asymptotic growth of the number of rational points of bounded height on smooth projective split toric varieties with Picard rank 2 over number fields, with respect to Arakelov height functions associated with big metrized line…
The topological zeta function of a matroid is a rational function as well as a valuative invariant of the matroid, encoding rich combinatorial information. We analyze topological zeta functions of matroids from the vantage point of several…
I give a formula for the zeta function of a projective toric hypersurface over a finite field and estimate its Newton polygon. As an application this formula allows us to compute the exact number of rational points on the families of…
In this paper, we give an overview of the various general methods in computing the zeta function of an algebraic variety defined over a finite field, with an emphasis on computing the reduction modulo $p^m$ of the zeta function of a…
We establish asymptotic formulas for the number of integral points of bounded height on partial equivariant compactifications of vector groups.
We establish the equivalence of three notions of $\mathbb{F}_q$-rational points on weighted projective spaces $\mathbb{P}_{\mathbf{w}}^n$ and derive explicit combinatorial formulas for their enumeration, leveraging Burnside's lemma and gcd…