Abstract:
We prove a new estimate for homogeneous linear forms with integer coefficients
in the logarithms of algebraic numbers. We obtain a qualitative improvement
of the estimate depending on the coefficients of the linear form and the best
value of the constant in the estimate in the case when the number
of logarithms is not too large.
\Bibitem{Ale08}
\by Yu.~M.~Aleksentsev
\paper The Hilbert polynomial and linear forms in the logarithms of algebraic numbers
\jour Izv. Math.
\yr 2008
\vol 72
\issue 6
\pages 1063--1110
\mathnet{http://mi.mathnet.ru/eng/im757}
\crossref{https://doi.org/10.1070/IM2008v072n06ABEH002429}
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Linking options:
https://www.mathnet.ru/eng/im757
https://doi.org/10.1070/IM2008v072n06ABEH002429
https://www.mathnet.ru/eng/im/v72/i6/p5
This publication is cited in the following 13 articles:
Andrej Dujella, Developments in Mathematics, 79, Diophantine m-tuples and Elliptic Curves, 2024, 167
Maurice Mignotte, Paul Voutier, “A kit for linear forms in three logarithms”, Math. Comp., 93:348 (2023), 1903
Rihane S.E., Luca F., Togbe A., “There Are No Diophantine Quadruples of Pell Numbers”, Int. J. Number Theory, 18:01 (2022), 27–45
Bonciocat N.C., Cipu M., Mignotte M., “There Is No Diophantine D(-1)\$D(-1)$-Quadruple”, J. Lond. Math. Soc.-Second Ser., 105:1 (2022), 63–99
Cipu M., Filipin A., Fujita Ya., “Diophantine Pairs That Induce Certain Diophantine Triples”, J. Number Theory, 210 (2020), 433–475
Trebjesanin M.B., Filipin A., “Nonexistence of D(4)-Quintuples”, J. Number Theory, 194 (2019), 170–217
Phulpoto A.H., Ahmed I., Soomro I., Hameed A., Muhammed R., Jokhio I.A., Chohan R., Kalhoro A.N., Phulpoto Sh.N., Jumani A.D., “Some Polynomial Formula of the Diophantine Quadruple With D(N) Property”, Int. J. Comput. Sci. Netw. Secur., 19:4 (2019), 249–251
Ziegler V., “Effective Results For Linear Equations in Members of Two Recurrence Sequences”, Acta Arith., 190:2 (2019), 139–169
Bugeaud Y., “Linear Forms in Logarithms and Applications”, Linear Forms in Logarithms and Applications, Irma Lectures in Mathematics and Theoretical Physics, 28, Eur. Math. Soc., 2018, 1–224
Fujita Ya., Luca F., “There Are No Diophantine Quadruples of Fibonacci Numbers”, Acta Arith., 185:1 (2018), 19–38
Bliznac M., Filipin A., “An Upper Bound For the Number of Diophantine Quintuples”, Bull. Aust. Math. Soc., 94:3 (2016), 384–394
Cipu M., Trudgian T., “Searching for Diophantine quintuples”, Acta Arith., 173:4 (2016), 365–382
Tim Trudgian, “Bounds on the number of Diophantine quintuples”, Journal of Number Theory, 2015
Citation in format AMSBIB
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