6533b7defe1ef96bd1275d4c

RESEARCH PRODUCT

Counting and equidistribution in quaternionic Heisenberg groups

Jouni ParkkonenFrédéric Paulin

subject

Mathematics - Differential GeometryPure mathematicsMathematics::Dynamical SystemsGeneral MathematicsHyperbolic geometryMathematics::Number Theory[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dimension (graph theory)11E39 11F06 11N45 20G20 53C17 53C22 53C55[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Equidistribution theorem01 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]differentiaaligeometriaSet (abstract data type)Light cone0103 physical sciences0101 mathematics[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]MathematicslukuteoriaQuaternion algebraMathematics - Number Theory010102 general mathematicsryhmäteoriaHermitian matrix[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]Action (physics)010307 mathematical physicsMathematics::Differential Geometry[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

description

AbstractWe develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

yearjournalcountryeditionlanguage
2020-01-09
http://arxiv.org/abs/1912.09690