131 Citations
Geometry-of-numbers methods in the cusp
- Mathematics
- 2021
. In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We illustrate these…
GEOMETRY-OF-NUMBERS METHODS IN THE CUSP AND APPLICATIONS TO CLASS GROUPS
- Mathematics
- 2021
In this article, we compute the mean number of 2-torsion elements in class groups of monogenized cubic orders, when such orders are enumerated by height. In particular, we show that the average size…
Mean value of the class number in function fields revisited
- Materials ScienceMonatshefte für Mathematik
- 2018
In this paper an asymptotic formula for the sum ∑L(1,χ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…
Mean value of the class number in function fields revisited
- Mathematics
- 2018
In this paper an asymptotic formula for the sum $$\sum L(1,\chi )$$∑L(1,χ) is established for the family of quadratic Dirichlet L-functions over the rational function field over a finite field…
Paramétrisation de structures algébriques et densité de discriminants
- Mathematics
- 2005
La composition de Gauss donne une structure de groupe aux orbites de formes quadratiques binaires entieres de discriminant D, sous l'action de SL 2 par changement de variable, essentiellement le…
Artin representations of Q of dihedral type
- Mathematics
- 2016
Equivalently, for a positive integer N , the number of isomorphism classes of two-dimensional irreducible monomial Artin representations of Q of conductor N is on average κN . By contrast, if we…
LAWS OF COMPOSITION AND ARITHMETIC STATISTICS: FROM GAUSS TO BHARGAVA
- Mathematics
- 2015
γ · f(x, y) = f((x, y) · γ) , where γ ∈ SL2(Z) and f is an integral binary quadratic form. This action preserves the discriminant ∆ = b − 4ac of binary quadratic forms, i.e., ∆(f) = ∆(γ · f). Gauss…
SELF-DUAL ARTIN REPRESENTATIONS
- Mathematics
- 2012
Functional equations in number theory are relations between an L-function and some sort of dual L-function, and in general, the L-function and its dual need not coincide. For example, if χ is a…
Momente der Klassenzahlen binärer quadratischer Formen mit ganzalgebraischen Koeffizienten
- 2006
(vgl. Barban [1]). Ziel der vorliegenden Arbeit ist folgende Verallgemeinerung von (1): k sei totalreeller Zahlkörper mit ungerader Klassenzahl. Sei Ok der Ring der ganzen Zahlen in k, E(Ok) seine…