scholarly journals Generalizations of Jacobsthal sums and hypergeometric series over finite fields

2021 ◽  
Author(s):  
Pramod Kumar Kewat ◽  
Ram Kumar
Keyword(s):  
Finite Fields ◽  
Hypergeometric Series

Appell series 𝔽1 over finite fields

2018 ◽  
Vol 14 (03) ◽  
pp. 727-738 ◽  
Author(s):  
Long Li ◽  
Xin Li ◽  
Rui Mao
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Generating Functions ◽  
Hypergeometric Series

In 1987, Greene introduced the notion of the finite field analogue of hypergeometric series. In this paper, we give a finite field analogue of Appell series and obtain some transformation and reduction formulas. We also establish the generating functions for Appell series over finite fields.

scholarly journals Certain transformations for hypergeometric series in the p-adic setting

2015 ◽  
Vol 11 (02) ◽  
pp. 645-660 ◽  
Author(s):  
Rupam Barman ◽  
Neelam Saikia
Keyword(s):  
Elliptic Curves ◽  
Finite Fields ◽  
Gamma Function ◽  
Hypergeometric Functions ◽  
Hypergeometric Series ◽  
Transformation Formulas ◽  
Trace Of Frobenius

In [The trace of Frobenius of elliptic curves and the p-adic gamma function, Pacific J. Math. 261(1) (2013) 219–236], McCarthy defined a function nGn[⋯] using the Teichmüller character of finite fields and quotients of the p-adic gamma function. This function extends hypergeometric functions over finite fields to the p-adic setting. In this paper, we give certain transformation formulas for the function nGn[⋯] which are not implied from the analogous hypergeometric functions over finite fields.

Appell’s hypergeometric series over finite fields

2019 ◽  
Vol 16 (04) ◽  
pp. 673-692
Author(s):  
Mohit Tripathi ◽  
Neelam Saikia ◽  
Rupam Barman
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Hypergeometric Series ◽  
Gauss Sums ◽  
Integral Representations

We define four functions [Formula: see text] and [Formula: see text] as finite field analogues of Appell series [Formula: see text] and [Formula: see text], respectively using purely Gauss sums in the spirit of finite field hypergeometric series introduced by McCarthy. We establish relations among [Formula: see text] and [Formula: see text] analogous to those satisfied by the classical Appell series. Recently, several people have defined finite field analogues of Appell series using integral representations of Appell series. We show that our functions [Formula: see text] and [Formula: see text] are closely related to those functions.

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields
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