\(p\)-adic gamma function and the trace of Frobenius of elliptic curves
type: Item
instance of: scholarly article
title: \(p\)-adic gamma function and the trace of Frobenius of elliptic curves
zbMATH Open document ID: 1345.11041
author: Rupam Barman
author: Neelam Saikia
published in: Journal of Number Theory
publication date: 2014-08-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.3321
review text: In [Pac. J. Math. 261, No. 1, 219--236 (2013; Zbl 1296.11079)], \textit{D. McCarthy} defined a function \(_n G_n[\cdots]\) using the Teichmüller character of finite fields and quotients of the \(p\)-adic gamma function and could express the trace of Frobenius of elliptic curves over a prime field in terms of special values of \(_2 G_2[\cdots]\). In the present article, the authors find two new formulas for the trace of elliptic curves over \(\mathbb{F}_q\), for an arbitrary \(q\), in terms of \(_2 G_2[\cdots]\) with different parameters. Hence, this can be seen as transformation formulas for McCarthy's result (which actually also holds more generally over \(\mathbb{F}_q\)).
reviewed by: Christophe Ritzenthaler
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 33E50
Mathematics Subject Classification ID: 33C99
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 11T24
zbMATH DE Number: 6334897
zbMATH Keywords: trace of Frobenius
zbMATH Keywords: elliptic curves
zbMATH Keywords: characters of finite fields
zbMATH Keywords: Gauss sums
zbMATH Keywords: Teichmüller character
zbMATH Keywords: \(p\)-adic gamma function
MaRDI profile type: Publication
OpenAlex ID: W2964229798
arXiv ID: 1304.3321
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DOI: 10.1016/J.JNT.2014.01.026
description: scientific article; zbMATH DE number 6334897