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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hypergeometric functions over finite fields


Author: John Greene
Journal: Trans. Amer. Math. Soc. 301 (1987), 77-101
MSC: Primary 11T21; Secondary 11L05, 33A35
MathSciNet review: 879564
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Abstract: In this paper the analogy between the character sum expansion of a complex-valued function over $ {\text{GF}}(p)$ and the power series expansion of an analytic function is exploited in order to develop an analogue for hypergeometric series over finite fields. It is shown that such functions satisfy many summation and transformation formulas analogous to their classical counterparts.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0879564-8
PII: S 0002-9947(1987)0879564-8
Article copyright: © Copyright 1987 American Mathematical Society