Traces of Frobenius on specific elliptic curve families equal weighted averages or values of p-adic hypergeometric functions, producing summation identities and p-adic transformation analogues.
Ireland and M.Rosen,A Classical introduction to modern number theory, 2nd ed, Springer, GTM Vol
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Weighted averages of $p$-adic hypergeometric functions and traces of Frobenius of elliptic curves
Traces of Frobenius on specific elliptic curve families equal weighted averages or values of p-adic hypergeometric functions, producing summation identities and p-adic transformation analogues.