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math.NT2002
Local points on P-adically uniformized Shimura varieties
Bruce W. Jordan, Ron Livné, Yakov Varshavsky
Using the p-adic uniformization of Shimura varieties we determine, for some of them, over which local fields they have rational points. Using this we show in some new curve cases t…
math.NT1999
The Ramanujan property for regular cubical complexes
Bruce W. Jordan, Ron Livné
This paper considers a higher-dimensional generalization of the notion of Ramanujan graphs, defined by Lubotzky, Phillips, and Sarnak. Specifically the Ramanujan property is studie…
math.NT1998
On Atkin-Lehner quotients of Shimura curves
Bruce W. Jordan, Ron Livné
Poonen and Stoll have shown that the reduced Shafarevich-Tate group of a principally polarized abelian variety over a global field can have order twice a square (the odd case) as w…