We consider certain CM elliptic curves which are related to Fermat curves, and express the values of L-functions at $$s=2$$ 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.
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