Traces of Hecke operators in level 1 and \(p\)-adic hypergeometric functions

DOI10.1007/s11139-019-00170-zzbMath1465.11108OpenAlexW2971590619WikidataQ127300035 ScholiaQ127300035MaRDI QIDQ780440

Sudhir Pujahari, Neelam Saikia

Publication date: 15 July 2020

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-019-00170-z

zbMATH Keywords

elliptic curvesGauss sums\(p\)-adic gamma functiontraces of Hecke operators\(p\)-adic hypergeometric functionstraces of Frobenius

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Curves over finite and local fields (11G20) Other character sums and Gauss sums (11T24) Fourier coefficients of automorphic forms (11F30) Special functions in characteristic (p) (gamma functions, etc.) (33E50)

Related Items (1)

Sato-Tate distribution of \(p\)-adic hypergeometric functions

Cites Work

• Nonsingular plane cubic curves over finite fields
• Gauss sums and the p-adic \(\Gamma\)-function
• The points of a certain fivefold over finite fields and the twelfth power of the eta function
• The trace of Frobenius of elliptic curves and the \(p\)-adic gamma function
• Modularity of a certain Calabi-Yau threefold
• Summation identities and special values of hypergeometric series in the \(p\)-adic setting
• Traces of Hecke operators in level 1 and Gaussian hypergeometric functions
• Hypergeometric functions over 𝔽_{𝕢} and traces of Frobenius for elliptic curves
• Bilateral $q$-Watson and $q$-Whipple sums
• EXTENDING GAUSSIAN HYPERGEOMETRIC SERIES TO THE p-ADIC SETTING
• Hypergeometric functions over ${\mathbb {F}_p}$ and relations to elliptic curves and modular forms
• Hypergeometric Functions Over Finite Fields
• The basis problem for modular forms on Γ₀(𝑁)
• Values of Gaussian hypergeometric series
• Combinatorics of traces of Hecke operators
• Vanishing and non-vanishing of traces of Hecke operators
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