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Linear forms in logarithms and integral points on higher-dimensional varieties [PDF]

Algebra & Number Theory, 2014
We apply inequalities from the theory of linear forms in logarithms to deduce effective results on S-integral points on certain higher-dimensional varieties when the cardinality of S is sufficiently small. These results may be viewed as a higher-dimensional version of an effective result of Bilu on integral points on curves.
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Linear forms in Logarithms and Diophantine equation

, 2022
The field of transcendance has a variety of subfields including : the transcendence of individual numbers, algebraic independence, transcendence of functions ( for example, modular forms, the zeta and $j$ functions, etc. ) at particular values, and applications to Diophantine equations which involve the linearly recurrent sequences (for example ...
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Lower bounds for linear forms in two p-adic logarithms

Journal of Number Theory
Given two algebraic numbers $\alpha_1,\alpha_2$, let $\Lambda=\{\alpha_1^{b_1}-\alpha_2^{b_2}:b_1,b_2\in\mathbb{Q}^+\}$. A well-studied problem is computing $\vert \Lambda\vert=\min_{\alpha\in \Lambda}\vert\alpha\vert$. In this paper, the author considers the $p$-adic absolute value \(\vert \Lambda\vert_p=\min\{\vert \alpha\vert_p:\alpha\in ...
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The Chabauty--Coleman method and p-adic linear forms in logarithms

, 2020
16 pages, comments ...
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Modular Galois representations and linear forms in abelian logarithms

, 2022
In this thesis, we study the properties of the residual Galois representations attached to modular forms, and the theory of linear forms in logarithms over abelian varieties. These are two distinct parts of number theory but they recently had joint application in the context of the resolution of Diophantine problems.In the first part of the thesis, we ...
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Linear forms in p-adic logarithms [PDF]

Acta Arithmetica, 1989
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A sharpening of the bounds for linear forms in logarithms [PDF]