Appell–Lauricella Hypergeometric Functions over Finite Fields, and a New Cubic Transformation Formula

2019 ◽  
pp. 417-422
Author(s):  
Sharon Frechette ◽  
Holly Swisher ◽  
Fang-Ting Tu
Keyword(s):  
Finite Fields ◽  
Hypergeometric Functions ◽  
Transformation Formula

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.

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