Related papers: Northcott numbers for the weighted Weil heights
Given a variety over $\mathbb{Q}$, we study the distribution of the number of primes dividing the coordinates as we vary an integral point. Under suitable assumptions, we show that this has a multivariate normal distribution. We generalise…
In this note we consider the distribution of values of weighted sums of the von Mangoldt arithmetical function. By using a formula for the distribution of values of trigonometric polynomials, we are able to present evidence supporting the…
For a smooth, projective complex variety, we introduce several mixed Hodge structures associated to higher algebraic cycles. Most notably, we introduce a mixed Hodge structure for a pair of higher cycles which are in the refined normalized…
We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial. The method we use is a blend of techniques coming from…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
We give a formula with explicit error term for the number of $K$-rational points $P$ satisfying $H(f(P)) \le X$ as $X \to \infty$, where $f$ is a nonconstant morphism between projective spaces defined over a number field $K$ and $H$ is the…
We formulate a conjectured orthogonality relation between the Fourier coefficients of Maass forms on PGL(N) for N>=2. Based on the work of Goldfeld-Kontorovich and Blomer for N=3, and on our conjecture for N>=4, we prove a weighted vertical…
This article derives several properties of the Riesz distributions, such as their corresponding Bartlett decompositions, the inverse Riesz distributions and the distribution of the generalised variance for real normed division algebras. In…
Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps most interesting of these weights, w_{12}, led to a recurrence relation and an identity for which he requested combinatorial…
We investigate the relationship between Geometric Invariant Theory (GIT) heights and weighted heights, with a focus on their interaction in weighted projective spaces and their application to binary forms. Building on the weighted height…
We revisit $R$-polynomials with introducing the new idea ``shifted $R$-polynomials" (or Bruhat weight) for all Bruhat intervals in finite Coxeter groups. Then, we apply these polynomials to weighted counting of Bruhat paths. Further, we…
We give an explicit formula for the Galois descent expressing multiple $t$-values of maximal height in terms of classical multiple zeta values, making precise Murakami's earlier motivic result. Our results rely on the theory of iterated…
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special…
Let $S$ be a set of $n$ points in general position in the plane, and let $X_{k,\ell}(S)$ be the number of convex $k$-gons with vertices in $S$ that have exactly $\ell$ points of $S$ in their interior. We prove several equalities for the…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…
We survey Weber's class number problem and its variants in the spirit of arithmetic topology; we recollect some history, present a relation to certain units and generalized Pell's equation, and overview a study of the $p$-adic limits of…
A number of hook formulas and hook summation formulas have previously appeared, involving various classes of trees. One of these classes of trees is rooted trees with labelled vertices, in which the labels increase along every chain from…
Let X be a smooth or proper variety defined over a finite field. The geometric etale fundamental group of X is a normal subgroup of the Weil group, so conjugation gives it a Weil action. We consider the pro-Q_l-algebraic completion of the…