On Eisenstein's formula for the Fermat quotient
John Blythe Dobson
TL;DR
This paper refines Eisenstein's 1850 representation of the Fermat quotient of base 2 as an alternating series, providing new evaluations and insights into its structure.
Contribution
It introduces new refinements and evaluations of Eisenstein's series representation of the Fermat quotient, expanding understanding of its properties.
Findings
New evaluations of the Fermat quotient series
Refined series representations with improved convergence
Enhanced understanding of Eisenstein's formula
Abstract
This paper presents some refinements of the representation of the Fermat quotient of base 2 as an alternating series which was discovered by Eisenstein in 1850, including some evaluations that are believed to be new.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Advanced Algebra and Geometry