A quadratic hypergeometric ${}_2\hspace {-1pt}F_1$ transformation over finite fields
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- by Ron Evans and John Greene PDF
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Abstract:
In 1984, the second author conjectured a quadratic transformation formula which relates two hypergeometric ${}_2\hspace {-1pt}F_1$ functions over a finite field $\mathbb {F}_q$. We prove this conjecture in Theorem 2. The proof depends on a new linear transformation formula for pseudo-hypergeometric functions over $\mathbb {F}_q$. Theorem 2 is then applied to give an elegant new transformation formula (Theorem 3) for ${}_2\hspace {-1pt}F_1$ functions over finite fields.References
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Additional Information
- Ron Evans
- Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
- MR Author ID: 64500
- Email: revans@ucsd.edu
- John Greene
- Affiliation: Department of Mathematics and Statistics, University of Minnesota–Duluth, Duluth, Minnesota 55812
- MR Author ID: 232833
- Email: jgreene@d.umn.edu
- Received by editor(s): October 30, 2015
- Received by editor(s) in revised form: November 5, 2015, November 18, 2015, and May 18, 2016
- Published electronically: October 18, 2016
- Communicated by: Matthew A. Papanikolas
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1071-1076
- MSC (2010): Primary 11T24, 33C05
- DOI: https://doi.org/10.1090/proc/13303
- MathSciNet review: 3589307