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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Hypergeometric functions over finite fields
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by John Greene PDF
Trans. Amer. Math. Soc. 301 (1987), 77-101 Request permission


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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 301 (1987), 77-101
  • MSC: Primary 11T21; Secondary 11L05, 33A35
  • DOI:
  • MathSciNet review: 879564