We consider certain CM elliptic curves which are related to Fermat curves, and express the values of L-functions at s = 2 in terms of special values of generalized hypergeometric functions. We compare them and a similar result of Rogers-Zudilin with Otsubo's regulator formulas, and give a new proof of the Beilinson conjectures originally due to Bloch.
In this paper, we consider L-functions of modular forms of weight 3, which are products of the Jacobi theta series, and express their special values at s = 3, 4 in terms of special values of Kampé de Fériet hypergeometric functions. Moreover, via L-values, we give some relations between special values of Kampé de Fériet hypergeometric functions and generalized hypergeometric functions.
In this paper, we consider a modular form of weight 3, which is a product of the Borweins theta series, and express its L-values at s = 1, 2 and 3 in terms of special values of Kampé de Fériet hypergeometric functions, which are two-variable generalization of generalized hypergeometric functions.
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