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4 Acta Arithmetica

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Commutative algebraic groups and p-adic linear forms

100%

Fuchs C. , Pham D.

nr 2

115-147

Let G be a commutative algebraic group defined over a number field K that is disjoint over K from $𝔾_{a}$ 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.

Perfect powers in linear recurring sequences

100%

Fuchs C. , Tichy R.

Acta Arithmetica

2003

tom 107

nr 1

9-25

An effective Shafarevich theorem for elliptic curves

80%

Fuchs C. , von Känel R. , Wüstholz G.

Acta Arithmetica

2011

tom 148

nr 2

189-203

Effective solution of the D(-1)-quadruple conjecture

80%

Dujella A. , Filipin A. , Fuchs C.

Acta Arithmetica

2007

tom 128

nr 4

319-338