Appell series over finite fields and modular forms. (English) Zbl 1535.33014
The author finds finite field analogues of classical identities involving classical \(F_4\)-Appell series and \({}_3F_2\)-classical hypergeometric series. In particular, he expresses the special values of \(F_4^{*}\), a finite field analogue of the classical Appell series \(F_4\), in terms of the Fourier coefficients of weight-three modular forms.
Reviewer: Lei Yang (Beijing)
MSC:
| 33C65 | Appell, Horn and Lauricella functions |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 33C20 | Generalized hypergeometric series, \({}_pF_q\) |
| 11F30 | Fourier coefficients of automorphic forms |
| 11F03 | Modular and automorphic functions |
Keywords:
hypergeometric series over finite fields; Appell series; Fourier coefficients of modular formsReferences:
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