18 citations · 54 across the 57 of their papers we have counts for
4 papers · 2 filters
On well-rounded ideal lattices - II
Lenny Fukshansky, Glenn Henshaw, Philip Liao +3
We study well-rounded lattices which come from ideals in quadratic number fields, generalizing some recent results of the first author with K. Petersen. In particular, we give a ch…
On integral well-rounded lattices in the plane
Lenny Fukshansky, Glenn Henshaw, Philip Liao +3
We investigate distribution of integral well-rounded lattices in the plane, parameterizing the set of their similarity classes by solutions of the family of Pell-type Diophantine e…
Well-rounded zeta-function of planar arithmetic lattices
Lenny Fukshansky
We investigate the properties of the zeta-function of well-rounded sublattices of a fixed arithmetic lattice in the plane. In particular, we show that this function has abscissa of…
Heights and quadratic forms: on Cassels' theorem and its generalizations
Lenny Fukshansky
In this survey paper, we discuss the classical Cassels' theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings,…