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20011005BuchAbelian approach to modular forms of neat 2ball lattices Holzapfel, RolfPeterIn previous papers [HoEis], [Ho2000] we found neat Picard modular surfaces with abelian minimal model and, conversely, a divisor criterion on abelian surfaces A for such a situation. For the corresponding ball lattices ...

20000328BuchCyclotomic Curve Families over Elliptic Curves with Complete PicardEinstein Metric Holzapfel, RolfPeterAccording to a problem of Hirzebruch we look for models of biproducts of elliptic CMcurves with Picard modular structure. We introduce the singular mean value of crossing elliptic divisors on surfaces and determine its ...

20011012BuchJacobi theta embedding of a hyperbolic 4space with cusps Holzapfel, RolfPeterStarting from a fixed elliptic curve with complex multiplication we compose lifted quotients of elliptic Jacobi theta functions to abelian functions in higher dimension. In some cases, where complete PicardEinstein metrics ...

20051104BuchOrbital Functional Series on Picard Surfaces Holzapfel, RolfPeterWe introduce orbital functionals $\int \boldsymbol{\beta} $ simultaneously for each commensurability class of orbital surfaces. They are realized on infinitely dimensional \emph{orbital} divisor spaces spanned by ...

19991210BuchPicardEinstein Metrics and Class Fields Connected with Apollonius Cycle Holzapfel, RolfPeter; Piñeiro, A.; Vladov, N.We define PicardEinstein metrics on complex algebraic surfaces as KählerEinstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along ...

19980817BuchPicardEinstein Metrics and Class Fields Connected with Apollonius Cycle Holzapfel, RolfPeterWe define Picard_Einstein metrics on complex algebraic surfaces as KählerEinstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along ...

20051107BuchQuadricLine Configurations Degenerating Plane Picard Einstein Metrics III Holzapfel, RolfPeter; Vladov, N.We define PicardEinstein metrics on complex algebraic surfaces as KählerEinstein metrics with negative constant sectional curvature pushed down from the complex unit ball allowing degenerations along cycles. We ...

20051026BuchSymplectic representation of a braid group on 3sheeted covers of the Riemann sphere Holzapfel, RolfPeterWhy we called the class of twodimensional Shimura varieties, which are not Hilbert modular, "Picard modular surfaces" ? In the mean time the name has been generally accepted, see e.g. Langlands (and others) [LR]. On the ...

20010215BuchThe Emergence of Picard Jacobians in Cryptography Sarlabous, Jorge Estrada; Cherdieu, JeanPierre; Barreiro, Ernesto Reinaldo; Holzapfel, RolfPeterIn this paper we present a new family of Jacobian Varieties defined over finite fields that provides many elements whose group structure is suitable for cryptosystems based on the intractability of the discrete logarithm ...

19970509BuchZeta Dimension Formula for Picard Modular Cusp Forms of Neat Natural Congruence Subgroups Holzapfel, RolfPeter