A relative Dobrowolski lower bound over abelian extensions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 29 (2000) no. 3, pp. 711-727.
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     author = {Amoroso, Francesco and Zannier, Umberto},
     title = {A relative {Dobrowolski} lower bound over abelian extensions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {711--727},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {3},
     year = {2000},
     mrnumber = {1817715},
     zbl = {1016.11026},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_3_711_0/}
}
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Amoroso, Francesco; Zannier, Umberto. A relative Dobrowolski lower bound over abelian extensions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 29 (2000) no. 3, pp. 711-727. http://www.numdam.org/item/ASNSP_2000_4_29_3_711_0/

[Am-Da1] F. Amoroso - S. David, Le problème de Lehmer en dimension supérieure, J. reine angew. Math. 513 (1999), 145-179. | MR | Zbl

[Am-Da2] F. Amoroso - S. David, Minoration de la hauteur normalisée des hypersurfaces, Acta Arith. 92 (2000), no. 4, 340-366. | MR | Zbl

[Am-Dv] F. Amoroso - R. Dvornicich, A lower bound for the height in Abelian extensions, J. Number Theory 80 (2000), no. 2, 260-272. | MR | Zbl

[Bo] D. Boyd, Kronecker's theorem and Lehmer's problem for polynomials in several variables, J. Number Theory 13 (1980), 116-121. | MR | Zbl

[Da-Ph] P. Philippon - S. David, Minorations des hauteurs normalisées des sous-variétés des tores, Ann. Scuola Norm. Sup. Pisa a. Sci (4) 28 (1999), 489-543. | Numdam | MR | Zbl

[Do] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401. | MR | Zbl

[Lau] M. Laurent, Equations diophantiennes exponentielles, Invent. Math. 78 (1984), 299-327. | MR | Zbl

[Law] W. Lawton, A generalization of a theorem of Kronecker, J. of the Science Faculty of Chiangmai University (Thailand) 4 (1977), 15-23. | Zbl

[Le] D.H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. 34 (1933), 461-479. | JFM | MR | Zbl

[Na] W. Narkiewicz, "Elementary and analytic theory of algebraic numbers", Second edition, Springer-Verlag, Berlin, PWN-Polish Scientific Publishers, Warsaw, 1990. | MR | Zbl

[No] N. Northcott, An inequality in the theory of arithmetic on algebraic varieties, Proc. Camb. Philos. Soc. 45 (1949), 502-509. | MR | Zbl

[Ra] U. Rausch, On a theorem of Dobrowolski about the product of conjugate numbers, Colloq. Math. 50 (1985), no. 1, 137-142. | MR | Zbl

[Ro-Th] D. Roy - J. Thunder, An absolute Siegel's lemma, J. reine angew. Math. 476 (1996), 1-12. | MR | Zbl

[Schi] A. Schinzel, On the product of the conjugates outside the unit circle of an algebraic number, Acta Arith. 24 (1973), 385-399. Addendum, ibid. 26 (1973), 329-361. | MR | Zbl

[Schm] W.M. Schmidt, "Diophantine approximations and Diophantine equations", Lecture Notes in Mathematics 1467, Springer-Verlag, Berlin, 1991. | MR | Zbl

[Sm] C.J. Smyth, A Kronecker-type theorem for complex polynomials in several variables, Canad. Math. Bull. 24 (1981), 447-452. Errata, ibid. 25 (1982), 504. | MR | Zbl

[Wa] L.C. Washington, "Introduction to Cyclotomic Fields", Springer-Verlag, New York, 1982. | MR | Zbl

[Zh] S. Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. 136 (1992), 569-587. | MR | Zbl