3 papers
math.DG2024
Divergent geodesics, ambiguous closed geodesics and the binary additive divisor problem
Jouni Parkkonen, Frédéric Paulin
We give an asymptotic formula as for the number of common perpendiculars of length at most between two divergent geodesics or a divergent geodesic and a compact l…
math.NT2010
On the representation of integers by indefinite binary Hermitian forms
Jouni Parkkonen, Frédéric Paulin
Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representation…
math.DG2010
On strictly convex subsets in negatively curved manifolds
Jouni Parkkonen, Frédéric Paulin
In a complete simply connected Riemannian manifold X of pinched negative curvature, we give a sharp criterion for a subset C to be the epsilon-neighbourhood of some convex subset o…