Smyth, Christopher J. Totally positive algebraic integers of small trace. (English) Zbl 0534.12002 Ann. Inst. Fourier 34, No. 3, 1-28 (1984). Let \(\alpha\) be a totally positive algebraic integer, with the difference between its trace and its degree at most 6. We describe an algorithm for finding all such \(\alpha\), and display the resulting list of 1314 values of \(\alpha\) which the algorithm produces. Reviewer: Chris Smyth (Edinburgh) Cited in 1 ReviewCited in 26 Documents MSC: 11R04 Algebraic numbers; rings of algebraic integers 11R80 Totally real fields Keywords:difference between trace and degree at most 6; list of values; totally positive algebraic integer; algorithm PDF BibTeX XML Cite \textit{C. J. Smyth}, Ann. Inst. Fourier 34, No. 3, 1--28 (1984; Zbl 0534.12002) Full Text: DOI Numdam EuDML OpenURL References: [1] E.W. CHENEY, Introduction to approximation theory, McGraw-Hill, New York, 1966. · Zbl 0161.25202 [2] R.M. ROBINSON, Algebraic equations with span less than 4, Math. of Comp., 10 (1964), 549-559. · Zbl 0147.12905 [3] C.L. SIEGEL, The trace of totally positive and real algebraic integers, Ann Math., 46 (1945), 302-312. · Zbl 0063.07009 [4] C.J. SMYTH, On the measure of totally real algebraic integers II, Math. of Comp., 37 (1981), 205-208. · Zbl 0475.12001 [5] C.J. SMYTH, The mean values of totally real algebraic integers, Math. of Comp., to appear April 1984. · Zbl 0536.12006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.