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Hypergeometric functions over \(\mathbb F_q\) and traces of Frobenius for elliptic curves. (English) Zbl 1319.11090

Summary: We present explicit relations between the traces of Frobenius endomorphisms of certain families of elliptic curves and special values of \(_2F_1\)-hypergeometric functions over \(\mathbb F_q\) for \(q\equiv 1\pmod 6\) and \(q\equiv 1\pmod 4\).

MSC:

11T24 Other character sums and Gauss sums
11G20 Curves over finite and local fields
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