| Popis: |
Legendre module λ, Feigenbaum constant δF and αF and modular units g(u) depend on principal ideals of complex multiplication (CM). The Hermite problem for cubic irrationalities is treated by quaternary continued fractions (QCF). Point addition on elliptic curves is generalized to CM via QCF showing λ- invariances and a power tower of modular units g(u) . Statistical λ- fluctuations on d-dimensional hypersurfaces Sd (d≤5) shape a pseudo- periodic contour CM. A transcendent vs. algebraic treatment of δF, αF and λ depends on topological entropy of CM. Periodic cycles on disk segments of Sd yield invariant in agreement with computation. |
