Special values of hypergeometric functions and periods of CM elliptic curves

الأصل · EN

Let X₀⁶(1)/W₆ be the Atkin-Lehner quotient of the Shimura curve X₀⁶(1) associated to a maximal order in an indefinite quaternion algebra of discriminant 6 over Q. By realizing modular forms on X₀⁶(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 with complex multiplication.