12:45
We consider the one parameter mirror families W of the Calabi-Yau 3-folds with Picard-Fuchs equations of hypergeometric type. By mirror symmetry the even D-brane masses of orginial Calabi-Yau manifolds M can be identified with four periods with respect to an integral symplectic basis of H3(W,Z) at the point of maximal unipotent monodromy. We establish that the masses of the D4 and D2 branes at the conifold are given by the two algebraically independent values of the L-function of the weight four holomorphic Hecke eigenform with eigenvalue one of Γ0(N). For the quintic in P4 it this Hecke eigenform of Γ0(25) was as found by Chad Schoen. It was discovered by de la Ossa, Candelas and Villegas that its coefficients ap count the number of solutions of the mirror quinitic at the conifold over the finite number field Fp . Using the theory of periods and quasi-periods of Γ0(N) and the special geometry pairing on Calabi-Yau 3 folds we can fix further values in the connection matrix between the maximal unipotent monodromy point and the conifold point.