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Zeros of $p$-adic
hypergeometric functions, $p$-adic analogues of Kummer's and
Pfaff's identities
Neelam Saikia |
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Vol. 307 (2020), No. 2, 491–510
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Abstract |
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We classify all the zeros and nonzero values of a family of hypergeometric series in the -adic setting. These values of hypergeometric series in the -adic setting lead to transformations of hypergeometric series in the -adic setting which can be described as -adic analogues of Kummer’s and Pfaff’s linear transformations on classical hypergeometric series. We also evaluate certain summation identities for hypergeometric series in the -adic setting as well as Gaussian hypergeometric series. |
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Keywords
character sum, Gauss sums, Jacobi sums, $p$-adic gamma
function
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Mathematical Subject Classification 2010
Primary: 11S80, 11T24, 33C20, 33C99, 33E50
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Milestones
Received: 19 March 2020
Revised: 1 May 2020
Accepted: 1 May 2020
Published: 4 September 2020
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Authors |
| Neelam Saikia | |
| Department of Mathematics Indian Institute of Technology Guwahati North Guwahati Assam India |
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