On Ramanujan Discriminant Modular Form

The cusp form of weight 12 for the full modular group, the so called Ramanujan ∆ is very important in number theory and its coefficients called Ramanujan tau function are very mysterious and enjoy many congruences modulus different prime numbers. Many of these congruences was proven in twentieth century. Ac_x0002_cording to a result of Swinnertondyer the reduction of Cusp form ∆ modulo 11 gives us a weight 2 modular and he obtained a spe_x0002_cial elliptic curve which become modular by ∆ mod 11, Inspired by this work we also predict that for other primes we should also obtain a Calabi-Yau varieties (the generalization of elliptic curves to higher dimensions) which are modular by reducing Ramanujan ∆ modulus to that prime. As a result of the existence of such Calabi-Yau varieties we can obtain new congruences for the Ra_x0002_manujan tau function in terms of the number of points of these Calabi-Yau varieties over the finite field Fp.