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<p>In this paper, we obtain a finite field analog for a transformation satisfied by <sub>2</sub><InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2024_980_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(F_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>F</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-classical hypergeometric series. We use properties of character sums over finite fields to deduce these results. Using these, we further evaluate certain special values for hypergeometric series over finite fields.</p>

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A transformation and certain special values of hypergeometric series over finite fields

  • 期刊论文

  • 发表日期：

    2025年1月28日

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  • Gautam Kalita,
  • Shaik Azharuddin

摘要

In this paper, we obtain a finite field analog for a transformation satisfied by 2 \(F_1\) F 1 -classical hypergeometric series. We use properties of character sums over finite fields to deduce these results. Using these, we further evaluate certain special values for hypergeometric series over finite fields.