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We describe Beilinson regulators of hypergeometric fibrations in terms of generalized hypergeometric functions. Employing a formula of Rogers and Zudilin, we obtain the comparison of the regulator with the special value of L function of a certain elliptic curve. This is a new approach toward the Beilinson conjecture.
We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be employed to compute periods of modular curves. This technique obviates the use of Hecke operators, and therefore provides a method for studying noncongruence modular...
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