Plus and minus logarithms and Amice transform
Cedric Dion, Antonio Lei

TL;DR
This paper provides a new distribution-based description of Pollack's plus and minus p-adic logarithms, including explicit formulas and connections to earlier distributions, and extends the approach to Loeffler's two-variable analogues.
Contribution
It introduces explicit distribution formulas for plus and minus p-adic logarithms and generalizes the description to Loeffler's two-variable versions.
Findings
Distribution formulas for plus and minus logarithms
Identification of minus distribution with Koblitz's distribution
Extension to Loeffler's two-variable analogues
Abstract
We give a new description of Pollack's plus and minus -adic logarithms in terms of distributions. In particular, if denote the pre-images of under the Amice transform, we give explicit formulae for the values for all and all integers . Our formulae imply that the distribution agrees with a distribution studied by Koblitz in 1977. Furthermore, we show that a similar description exists for Loeffler's two-variable analogues of these plus and minus logarithms.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Analytic Number Theory Research
