On algebraic equations with all but one root in the interior of the unit circle. (English) Zbl 0042.01501
Keywords:
linear algebra, polynomials, formsReferences:
| [1] | Berwald, Über einige mit dem Satz von Kakeya verwandte Sätze, Math. Z., Berlin 37 pp 61– (1933) · Zbl 0006.24401 · doi:10.1007/BF01474562 |
| [2] | Brauer, On the irreducibility of polynomials with large third coefficients, Amer. J. Math. 70 pp 423– (1948) · Zbl 0035.00902 · doi:10.2307/2372341 |
| [3] | A. Brauer |
| [4] | Erdös, On a family of symmetric Bernoulli convolutions, Amer. J. Math. 61 pp 974– (1939) · JFM 65.1308.01 · doi:10.2307/2371641 |
| [5] | Hurwitz, Über einen Satz des Herrn Kakeya, Tǒhoku math. J. 4 pp 89– (1913/14) |
| [6] | Mathematische Werke 2 pp 626– (1933) |
| [7] | Lipka, Zur Theorie der algebraischen Gleichungen mit positiven Koeffizienten, Acta Litt. Sci. Univ., Szeged, Sect. Sci. math. 5 pp 78– (1931) |
| [8] | Lipka, Über die Irreduzibilität von Polynomen, Math. Ann., Berlin 118 pp 235– (1941-43) · Zbl 0013.38604 · doi:10.1007/BF01487363 |
| [9] | Mayer, Sur les équations algébriques, Nouv. Ann. Math., III. S. 10 pp 111– (1891) |
| [10] | Nagell, Über einige Irreduzibilitätskriterien, Norske Vid. Selsk. Forhdl., Trondheim 5 pp 121– (1931) |
| [11] | Perron, Neue Kriterien für die Irreduzibilität algebraischer Gleichungen, J. reine angew. Math. 132 pp 288– (1907) |
| [12] | Perron, Algebra II pp 34– (1933) |
| [13] | Pisot, La, répartition modulo 1 et les nombres algébriques, Ann. Scuola norm. sup. Pisa, II.s. 7 pp 205– (1938) |
| [14] | Salem, Sets of uniqueness and sets of multiplicity, Trans. Amer. math. Soc. 54 pp 218– (1943) · doi:10.1090/S0002-9947-1943-0008428-8 |
| [15] | Salem, A remarkable class of algebraic integers, Proof of a conjecture of Vijayaraghavan. Duke math. J. 11 pp 103– (1944) · Zbl 0063.06657 · doi:10.1215/S0012-7094-44-01111-7 |
| [16] | Siegel, Algebraic integers whose conjugates lie in the unit circle, Duke math. J. 11 pp 597– (1944) · Zbl 0063.07005 · doi:10.1215/S0012-7094-44-01152-X |
| [17] | Vijayaraghavan, On the fractional parts of the powers of a number, II. Proc. Cambridge philos. Soc. 37 pp 349– (1941) · JFM 67.0988.02 · doi:10.1017/S0305004100017989 |
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