A Gaussian hypergeometric series evaluation and Apéry number congruences

@article{Ahlgren2000AGH,
  title={A Gaussian hypergeometric series evaluation and Ap{\'e}ry number congruences},
  author={Scott Ahlgren and Ken Ono},
  journal={Crelle's Journal},
  year={2000},
  volume={2000},
  pages={187-212}
}
If p is prime, then let φp denote the Legendre symbol modulo p and let p be the trivial character modulo p. As usual, let n+1Fn(x)p := n+1Fn „ φp, φp, . . . , φp p, . . . , p | x « p be the Gaussian hypergeometric series over Fp. For n > 2 the non-trivial values of n+1Fn(x)p have been difficult to obtain. Here we take the first step by obtaining a simple formula for 4F3(1)p. As a corollary we obtain a result describing the distribution of traces of Frobenius for certain families of elliptic… 
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