Results 151 to 160 of about 13,300 (186)

Appell series over finite fields and modular forms

open access: closedFinite Fields and Their Applications, 2023
The author finds finite field analogues of classical identities involving classical \(F_4\)-Appell series and \({}_3F_2\)-classical hypergeometric series. In particular, he expresses the special values of \(F_4^{*}\), a finite field analogue of the classical Appell series \(F_4\), in terms of the Fourier coefficients of weight-three modular forms.
Mohit Tripathi
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Appell series over finite fields and Gaussian hypergeometric series

open access: closedResearch in the Mathematical Sciences, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohit Tripathi, Rupam Barman
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Appell series 𝔽1 over finite fields

open access: closedInternational Journal of Number Theory, 2017
In 1987, Greene introduced the notion of the finite field analogue of hypergeometric series. In this paper, we give a finite field analogue of Appell series and obtain some transformation and reduction formulas. We also establish the generating functions for Appell series over finite fields.
Long Li, Xin Li, Rui Mao
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Supercongruences for truncated Appell series

open access: closedColloquium Mathematicum, 2019
After defining the truncated Appell series \(F_1\) and \(F_2\) and recalling the \(p\)-adic Gamma function \(\Gamma_p(x)\), this paper establishes that, for any prime \(p \geq 5 \), \[ F_1 \left[ \tfrac12; \tfrac12, \tfrac12; 1; 1, 1 \right] _ \frac{ p-1}{2} \equiv p \pmod {p^2},\] \[ F_2 \left[ \tfrac12; \tfrac12, \tfrac12; 1, 1; 1, 1 \right] _ \frac{
Ji-Cai Liu
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