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Comp."],"abstract":"<p>\n                    We prove that the two smallest values of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h left-parenthesis alpha right-parenthesis plus h left-parenthesis StartFraction 1 Over 1 minus alpha EndFraction right-parenthesis plus h left-parenthesis 1 minus StartFraction 1 Over alpha EndFraction right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\n                              \u03b1\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mfrac>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mrow>\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mi>\n                                  \u03b1\n                                  \n                                <\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mfrac>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mfrac>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                            <\/mml:mfrac>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">h(\\alpha ) + h(\\frac {1}{1-\\alpha }) + h(1 - \\frac {1}{\\alpha })<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"0\">\n                        <mml:semantics>\n                          <mml:mn>0<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"0.4218 ellipsis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>0.4218<\/mml:mn>\n                            <mml:mo>\n                              \u2026\n                              \n                            <\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">0.4218\\dots<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"alpha\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03b1\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\alpha<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    any algebraic integer.\n                  <\/p>","DOI":"10.1090\/s0025-5718-98-00963-6","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"815-820","source":"Crossref","is-referenced-by-count":4,"title":["Orbits of algebraic numbers with low heights"],"prefix":"10.1090","volume":"67","author":[{"given":"Gregory","family":"Dresden","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","unstructured":"E. Bombieri, A van der Poorten, and J. Vaaler, Effective measures of irrationality for cubic extensions of number fields, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23 (1996), 211\u2013248."},{"issue":"4","key":"2","doi-asserted-by":"publisher","first-page":"453","DOI":"10.4153\/CMB-1981-069-5","article-title":"Speculations concerning the range of Mahler\u2019s measure","volume":"24","author":"Boyd, David W.","year":"1981","journal-title":"Canad. Math. Bull.","ISSN":"https:\/\/id.crossref.org\/issn\/0008-4395","issn-type":"print"},{"issue":"4","key":"3","doi-asserted-by":"publisher","first-page":"391","DOI":"10.4064\/aa-34-4-391-401","article-title":"On a question of Lehmer and the number of irreducible factors of a polynomial","volume":"34","author":"Dobrowolski, E.","year":"1979","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"4","doi-asserted-by":"crossref","unstructured":"D. H. Lehmer, Factorization of certain cyclotomic funcions, Ann. of Math. 34 (1933), 461\u2013479.","DOI":"10.2307\/1968172"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"809","DOI":"10.2307\/2154300","article-title":"The number of irreducible factors of a polynomial. I","volume":"339","author":"Pinner, Christopher G.","year":"1993","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"issue":"1","key":"6","doi-asserted-by":"publisher","first-page":"137","DOI":"10.4064\/cm-50-1-137-142","article-title":"On a theorem of Dobrowolski about the product of conjugate numbers","volume":"50","author":"Rausch, Ulrich","year":"1985","journal-title":"Colloq. 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