1995
DOI: 10.1006/jnth.1995.1141
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Formes linéaires en deux logarithmes et déterminants d′interpolation

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Cited by 196 publications
(225 citation statements)
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“…We reproduce Corollaire 3 of [14] and Corollary 2.4 of [13], with minor simplification, in the special case where the algebraic numbers involved are rational.…”
Section: Proof Of Theorem 21mentioning
confidence: 99%
See 1 more Smart Citation
“…We reproduce Corollaire 3 of [14] and Corollary 2.4 of [13], with minor simplification, in the special case where the algebraic numbers involved are rational.…”
Section: Proof Of Theorem 21mentioning
confidence: 99%
“…For instance, the paper [11] can be regarded as the p-adic analogue of [14], although [14] includes a parameter log E while [11] does not. A parameter also called log E appeared for the first time in the p-adic setting in [8] and allows one to get better estimates when the rational numbers involved in the linear form are p-adically close to 1.…”
Section: Introductionmentioning
confidence: 99%
“…Finally from the inequalities We shall combine Lemma 5.8 with the following sharp estimate for two logarithms (Corollary 1 in [16]). Further similar estimates are easy to produce.…”
Section: Appendix From 2 To N Logarithmsmentioning
confidence: 99%
“…The proof for this range took about 3 hours. Going up to p < 10 6 is indeed overkill, since a careful application of linear forms in logarithms [23] to this problem shows that p < 8200 if y = −1. Thus we know for any p that is not in our range (and indeed for p > 8200) that y = −1 and we easily see that r = ±1 in all cases.…”
Section: 'Predicting Exponents Of Constants'mentioning
confidence: 99%
“…Using this information, another careful application of linear forms in logarithms [23] shows that p < 1237.…”
Section: 'Predicting Exponents Of Constants'mentioning
confidence: 99%