Number of \(\mathbb{F}_q\)-points on diagonal hypersurfaces and hypergeometric function

DOI10.1142/s1793042124501239MaRDI QIDQ6652050

Rupam Barman, Sulakashna

Publication date: 12 December 2024

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

hypergeometric seriescharacter sumdiagonal hypersurfaces\(p\)-adic gamma function

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Other character sums and Gauss sums (11T24) Varieties over finite and local fields (11G25) Special functions in characteristic (p) (gamma functions, etc.) (33E50)

Cites Work

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• Counting points over finite fields and hypergeometric functions
• \(p\)-adic gamma function and the trace of Frobenius of elliptic curves
• The number of \(\mathbb F_p\)-points on Dwork hypersurfaces and hypergeometric functions
• Gauss sums and the p-adic \(\Gamma\)-function
• Summation identities and transformations for hypergeometric series
• The trace of Frobenius of elliptic curves and the \(p\)-adic gamma function
• A complete hypergeometric point count formula for Dwork hypersurfaces
• Hypergeometric functions and relations to Dwork hypersurfaces
• COUNTING POINTS ON DWORK HYPERSURFACES AND -ADIC HYPERGEOMETRIC FUNCTIONS
• Hypergeometric functions over ${\mathbb {F}_p}$ and relations to elliptic curves and modular forms
• Hypergeometric Functions Over Finite Fields
• Exponential Sums and Differential Equations. (AM-124)

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\(p\)-adic hypergeometric functions and certain weight three newforms

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