SPECIAL VALUES OF HYPERGEOMETRIC FUNCTIONS AND PERIODS OF CM ELLIPTIC CURVES

Let X-0(6)(1)/W-6 be the Atkin-Lehner quotient of the Shimura curve X-0(6)(1) associated to a maximal order in an indefinite quaternion algebra of discriminant 6 over Q. By realizing modular forms on X-0(6)(1)/W6 in two ways, one in terms of hypergeometric functions and the other in terms of Borcherds forms, and using Schofer's formula for values of Borcherds forms at CM-points, we obtain special values of certain hypergeometric functions in terms of periods of elliptic curves over (Q) over bar with complex multiplication.