All the periodic points of a certain algebraic function related to the Rogers-Ramanujan continued fraction r(τ) are explicitly determined. This yields a new class number formula for orders in the fields K_d. Conjecture 1 of Part I is proved for the prime p=5, showing that the ring class fields over fields of type K_d whose conductors are relatively prime to 5 coincide with the fields generated over Q by the periodic points (excluding -1) of a fixed 5-adic algebraic function.

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