Algebraic integers whose conjugates lie near the unit circle
Bulletin de la Société Mathématique de France, Tome 106 (1978), pp. 169-176.
@article{BSMF_1978__106__169_0,
     author = {Stewart, Cameron L.},
     title = {Algebraic integers whose conjugates lie near the unit circle},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {169--176},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {106},
     year = {1978},
     doi = {10.24033/bsmf.1868},
     zbl = {0396.12002},
     mrnumber = {507748},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.1868/}
}
TY  - JOUR
AU  - Stewart, Cameron L.
TI  - Algebraic integers whose conjugates lie near the unit circle
JO  - Bulletin de la Société Mathématique de France
PY  - 1978
SP  - 169
EP  - 176
VL  - 106
PB  - Société mathématique de France
UR  - https://www.numdam.org/articles/10.24033/bsmf.1868/
DO  - 10.24033/bsmf.1868
LA  - en
ID  - BSMF_1978__106__169_0
ER  - 
%0 Journal Article
%A Stewart, Cameron L.
%T Algebraic integers whose conjugates lie near the unit circle
%J Bulletin de la Société Mathématique de France
%D 1978
%P 169-176
%V 106
%I Société mathématique de France
%U https://www.numdam.org/articles/10.24033/bsmf.1868/
%R 10.24033/bsmf.1868
%G en
%F BSMF_1978__106__169_0
Stewart, Cameron L. Algebraic integers whose conjugates lie near the unit circle. Bulletin de la Société Mathématique de France, Tome 106 (1978), pp. 169-176. doi : 10.24033/bsmf.1868. https://www.numdam.org/articles/10.24033/bsmf.1868/

[1] Blanksby (P. E.) and Montgomery (H. L.). - Algebraic integers near the unit circle, Acta Arithm., Warszawa, t. 28, 1971, p. 355-369. | MR | Zbl

[2] Boyd (D. W.). - Small Salem numbers, Duke math. J., t. 44, 1977, p. 315-328. | MR | Zbl

[3] Dobrowolski (E.). - On the maximal modulus of conjugates of an algebraic integer, Bull. Acad. polon. Sc. (à paraître). | Zbl

[4] Kronecker (L.). - Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten, J. für reine und angew. Math., t. 53, 1857, p. 173-175. | Zbl

[5] Lehmer (D. H.). - Factorization of certain cyclotomic functions, Annals of Math., Series 2, t. 34, 1933, p. 461-479. | JFM | Zbl

[6] Mignotte (M.) and Waldschmidt (M.). - Linear forms in two logarithms and Schneider's method, Math. Annalen, t. 231, 1978, p. 241-267. | MR | Zbl

[7] Salem (R.). - A remarkable class of algebraic integers. Proof of a conjecture o Vijayaraghavan, Duke math. J., t. 11, 1944, p. 103-108. | MR | Zbl

[8] Siegel (C. L.). - Algebraic integers whose conjugates lie in the unit circle, Duke math. J., t. 11, 1944, p. 597-602. | MR | Zbl

[9] Smyth (C. J.). - On the product of the conjugates outside the unit circle of an algebraic integer, Bull. London math. Soc., t. 3, 1971, p. 169-175. | MR | Zbl

[10] Waldschmidt (M.). - Nombres transcendants. - Berlin, Springer-Verlag, 1974 (Lecture Notes in Mathematics, 402). | Zbl

  • Looper, Nicole; Silverman, Joseph A Lehmer-type height lower bound for abelian surfaces over function fields, Transactions of the American Mathematical Society (2023) | DOI:10.1090/tran/9024
  • Khayutin, Ilya Non-vanishing of class group L-functions for number fields with a small regulator, Compositio Mathematica, Volume 156 (2020) no. 11, p. 2423 | DOI:10.1112/s0010437x20007472
  • Feng, Yuanyuan; Iyer, Gautam Dissipation enhancement by mixing, Nonlinearity, Volume 32 (2019) no. 5, p. 1810 | DOI:10.1088/1361-6544/ab0e56
  • Akhtari, Shabnam; Aktaş, Kevser; Biggs, Kirsti D.; Hamieh, Alia; Petersen, Kathleen; Thompson, Lola Lower Bounds for Heights in Relative Galois Extensions, Women in Numbers Europe II, Volume 11 (2018), p. 1 | DOI:10.1007/978-3-319-74998-3_1
  • Peled, Ron; Sen, Arnab; Zeitouni, Ofer Double roots of random littlewood polynomials, Israel Journal of Mathematics, Volume 213 (2016) no. 1, p. 55 | DOI:10.1007/s11856-016-1328-3
  • Verger-Gaugry, Jean-Louis On the Conjecture of Lehmer, Limit Mahler Measure of Trinomials and Asymptotic Expansions, Uniform distribution theory, Volume 11 (2016) no. 1, p. 79 | DOI:10.1515/udt-2016-0006
  • Waldschmidt, Michel Auxiliary functions in transcendental number theory, The Ramanujan Journal, Volume 20 (2009) no. 3, p. 341 | DOI:10.1007/s11139-009-9204-y
  • Silverman, Joseph H. A lower bound for the canonical height on elliptic curves over abelian extensions, Journal of Number Theory, Volume 104 (2004) no. 2, p. 353 | DOI:10.1016/j.jnt.2003.07.001
  • Masser, David Heights, Transcendence, and Linear Independence on Commutative Group Varieties, Diophantine Approximation, Volume 1819 (2003), p. 1 | DOI:10.1007/3-540-44979-5_1
  • Silverman, Joseph H. Small Salem Numbers, Exceptional Units, and Lehmer's Conjecture, Rocky Mountain Journal of Mathematics, Volume 26 (1996) no. 3 | DOI:10.1216/rmjm/1181072040
  • Silverman, Joseph H. Exceptional Units and Numbers of Small Mahler Measure, Experimental Mathematics, Volume 4 (1995) no. 1, p. 69 | DOI:10.1080/10586458.1995.10504309
  • Boyd, David W Kronecker's theorem and Lehmer's problem for polynomials in several variables, Journal of Number Theory, Volume 13 (1981) no. 1, p. 116 | DOI:10.1016/0022-314x(81)90033-0
  • Boyd, David W. Speculations Concerning the Range of Mahler's Measure, Canadian Mathematical Bulletin, Volume 24 (1980) no. 4, p. 453 | DOI:10.4153/cmb-1981-069-5
  • Smyth, C. J. On the measure of totally real algebraic integers, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 30 (1980) no. 2, p. 137 | DOI:10.1017/s1446788700016426
  • Anderson, M.; Masser, David W. Lower bounds for heights on elliptic curves, Mathematische Zeitschrift, Volume 174 (1980) no. 1, p. 23 | DOI:10.1007/bf01215078
  • Boyd, David W. Variations on a Theme of Kronecker, Canadian Mathematical Bulletin, Volume 21 (1978) no. 2, p. 129 | DOI:10.4153/cmb-1978-023-x

Cité par 16 documents. Sources : Crossref