The number of \(\mathbb F_p\)-points on Dwork hypersurfaces and hypergeometric functions

DOI10.1186/s40687-017-0096-yzbMath1410.11082arXiv1608.05697OpenAlexW2582319843WikidataQ59612596 ScholiaQ59612596MaRDI QIDQ521599

Dermot McCarthy

Publication date: 11 April 2017

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.05697

zbMATH Keywords

hypergeometric functionsDwork hypersurfaces

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)

Related Items (3)

Hypergeometric decomposition of symmetric \(K3\) quartic pencils ⋮ Hypergeometric functions over finite fields and modular forms. A survey and new conjectures ⋮ Dwork hypersurfaces of degree six and Greene's hypergeometric function

Cites Work

• Trace formulas for Hecke operators, Gaussian hypergeometric functions, and the modularity of a threefold
• Transformations of well-poised hypergeometric functions over finite fields
• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory.
• A family of Calabi-Yau varieties and potential automorphy
• Gauss sums and the p-adic \(\Gamma\)-function
• The trace of Frobenius of elliptic curves and the \(p\)-adic gamma function
• Summation identities and special values of hypergeometric series in the \(p\)-adic setting
• On the zeta function of a hypersurface. IV: A deformation theory for singular hypersurfaces
• Hypergeometric type identities in the $p$-adic setting and modular forms
• On a supercongruence conjecture of Rodriguez-Villegas
• Hypergeometric functions and relations to Dwork hypersurfaces
• COUNTING POINTS ON DWORK HYPERSURFACES AND -ADIC HYPERGEOMETRIC FUNCTIONS
• Gaussian hypergeometric evaluations of traces of Frobenius for elliptic curves
• Hypergeometric functions over ${\mathbb {F}_p}$ and relations to elliptic curves and modular forms
• A Gaussian hypergeometric series evaluation and Apéry number congruences
• On the Rationality of the Zeta Function of an Algebraic Variety
• Numbers of solutions of equations in finite fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The number of \(\mathbb F_p\)-points on Dwork hypersurfaces and hypergeometric functions