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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 6, Pages 5–52 (Mi izv757)  

This article is cited in 9 scientific papers (total in 9 papers)

The Hilbert polynomial and linear forms in the logarithms of algebraic numbers

Yu. M. Aleksentsev

Moscow State Institute of Steel and Alloys (Technological University)

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.

DOI: https://doi.org/10.4213/im757

Full text: PDF file (790 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2008, 72:6, 1063–1110

Bibliographic databases:

UDC: 511.3, 511.364, 511.51, 511.682
MSC: 11J86, 11J25, 11H06
Received: 30.01.2006

Citation: Yu. M. Aleksentsev, “The Hilbert polynomial and linear forms in the logarithms of algebraic numbers”, Izv. RAN. Ser. Mat., 72:6 (2008), 5–52; Izv. Math., 72:6 (2008), 1063–1110

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tim Trudgian, “Bounds on the number of Diophantine quintuples”, Journal of Number Theory, 2015  crossref  mathscinet  scopus
    2. Bliznac M., Filipin A., “An Upper Bound For the Number of Diophantine Quintuples”, Bull. Aust. Math. Soc., 94:3 (2016), 384–394  crossref  mathscinet  zmath  isi  elib  scopus
    3. Cipu M., Trudgian T., “Searching for Diophantine quintuples”, Acta Arith., 173:4 (2016), 365–382  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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  crossref  mathscinet  isi
    5. Fujita Ya., Luca F., “There Are No Diophantine Quadruples of Fibonacci Numbers”, Acta Arith., 185:1 (2018), 19–38  crossref  mathscinet  zmath  isi  scopus
    6. Trebjesanin M.B., Filipin A., “Nonexistence of D(4)-Quintuples”, J. Number Theory, 194 (2019), 170–217  crossref  mathscinet  zmath  isi  scopus
    7. 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  isi
    8. Ziegler V., “Effective Results For Linear Equations in Members of Two Recurrence Sequences”, Acta Arith., 190:2 (2019), 139–169  crossref  isi
    9. Cipu M., Filipin A., Fujita Ya., “Diophantine Pairs That Induce Certain Diophantine Triples”, J. Number Theory, 210 (2020), 433–475  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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