A relative Dobrowolski lower bound over abelian extensions

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1. [Am-Da1] F. Amoroso - S. David, Le problème de Lehmer en dimension supérieure, J. reine angew. Math. 513 (1999), 145-179. Zbl1011.11045MR1713323
2. [Am-Da2] F. Amoroso - S. David, Minoration de la hauteur normalisée des hypersurfaces, Acta Arith. 92 (2000), no. 4, 340-366. Zbl0948.11025MR1760242
3. [Am-Dv] F. Amoroso - R. Dvornicich, A lower bound for the height in Abelian extensions, J. Number Theory80 (2000), no. 2, 260-272. Zbl0973.11092MR1740514
4. [Bo] D. Boyd, Kronecker's theorem and Lehmer's problem for polynomials in several variables, J. Number Theory13 (1980), 116-121. Zbl0447.12003MR602452
5. [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. Zbl1002.11055MR1736526
6. [Do] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401. Zbl0416.12001MR543210
7. [Lau] M. Laurent, Equations diophantiennes exponentielles, Invent. Math.78 (1984), 299-327. Zbl0554.10009MR767195
8. [Law] W. Lawton, A generalization of a theorem of Kronecker, J. of the Science Faculty of Chiangmai University (Thailand) 4 (1977), 15-23. Zbl0447.12004
9. [Le] D.H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. 34 (1933), 461-479. Zbl0007.19904MR1503118JFM59.0933.03
10. [Na] W. Narkiewicz, "Elementary and analytic theory of algebraic numbers", Second edition, Springer-Verlag, Berlin, PWN-Polish Scientific Publishers, Warsaw, 1990. Zbl0717.11045MR1055830
11. [No] N. Northcott, An inequality in the theory of arithmetic on algebraic varieties, Proc. Camb. Philos. Soc.45 (1949), 502-509. Zbl0035.30701MR33094
12. [Ra] U. Rausch, On a theorem of Dobrowolski about the product of conjugate numbers, Colloq. Math.50 (1985), no. 1, 137-142. Zbl0579.12001MR818097
13. [Ro-Th] D. Roy - J. Thunder, An absolute Siegel's lemma, J. reine angew. Math. 476 (1996), 1-12. Zbl0860.11036MR1401695
14. [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. Zbl0275.12004MR360515
15. [Schm] W.M. Schmidt, "Diophantine approximations and Diophantine equations", Lecture Notes in Mathematics 1467, Springer-Verlag, Berlin, 1991. Zbl0754.11020MR1176315
16. [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. Zbl0475.12002MR644534
17. [Wa] L.C. Washington, "Introduction to Cyclotomic Fields", Springer-Verlag, New York, 1982. Zbl0484.12001MR718674
18. [Zh] S. Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. 136 (1992), 569-587. Zbl0788.14017MR1189866

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