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Acta Arithmetica
Article
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zbMATH Open
Article . 2015
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Acta Arithmetica
Article . 2015 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2014
License: arXiv Non-Exclusive Distribution
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Commutative algebraic groups and p-adic linear forms

Commutative algebraic groups and \(p\)-adic linear forms
Authors: Fuchs, Clemens; Pham, Duc Hiep;

Commutative algebraic groups and p-adic linear forms

Abstract

Let $G$ be a commutative algebraic group defined over a number field $K$ that is disjoint over $K$ to $\mathbb G_a$ and satisfies the condition of semistability. Consider a linear form $l$ on the Lie algebra of $G$ with algebraic coefficients and an algebraic point $u$ in a $p$-adic neighbourhood of the origin with the condition that $l$ does not vanish at $u$. We give a lower bound for the $p$-adic absolute value of $l(u)$ which depends up to an effectively computable constant only on the height of the linear form, the height of the point $u$ and $p$.

This is a preprint of the Materials accepted for publication in "Acta Arithmetica"

Keywords

Mathematics - Number Theory, 11G99 (Primary) 14L10, 11J86 (Secondary), Approximation in non-Archimedean valuations, heights, Arithmetic algebraic geometry (Diophantine geometry), Mathematics - Algebraic Geometry, effective results, FOS: Mathematics, linear forms, Number Theory (math.NT), Group varieties, Algebraic Geometry (math.AG), Linear forms in logarithms; Baker's method, commutative algebraic groups

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
bronze