Abstract
For primes $$p>3$$ we give a formula for the traces of pth Hecke operators on space of cusp forms of weight k and level 1 involving p-adic hypergeometric functions. We also express the traces of Frobenius for a certain family of elliptic curves in terms of p-adic hypergeometric function. Finally, we derive certain relations for Ramanujan’s $$\tau $$ -function and p-adic hypergeometric functions.
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