Small degree Salem numbers with trace −3

• Autorzy: Sac-Épée Jean-Marc

Identyfikatory

DOI

10.2478/candc-2023-0041

• Języki publikacji: EN

Abstrakty

EN

The contribution of this work is to provide tables of Salem numbers with trace −3 and small degrees, namely degrees 2d = 34, 36, 38, and 40. The implemented method also generates a list of totally positive polynomials of degrees d = 17, 18, 19, and 20, with trace 2d−3, a single root strictly greater than 4, and all other roots strictly between 0 and 4.

Słowa kluczowe

EN

Salem numbers of small trace; totally positive polynomials

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2023
• Tom: Vol. 52, No. 3
• Strony: 335--346
• Opis fizyczny: Bibliogr. 11 poz., tab.

Twórcy

autor

Sac-Épée Jean-Marc

• IECL, Université de Lorraine, France

Bibliografia

• Aguirre, J. and Peral, J. C. The trace problem for totally positive algebraic integers. London Math. Soc. Lecture Note Ser., 352.
• Cherubini, G. and Yatsyna, P. (2024) https://arxiv.org/pdf/2301.06536.pdf
• El Otmani, S., Maul, A., Rhin, G. and Sac-Épée, J.-M. (2014) Finding degree-16 monic irreducible integer polynomials of minimal trace by optimization methods. Exp. Math. 23, 1, 1–5.
• El Otmani, S., Rhin, G. and Sac-Épée, J.-M. (2015) A Salem number with degree 34 and trace −3. J. Number Theory 150, 21–25.
• Flammang, V. (2016) Une nouvelle minoration pour la trace absolue des entiers alg´ebriques totalement positifs. Note, hal-01346165.
• Flammang, V. (2019) Bounds for the trace of small Salem numbers. Rocky Mt. J. Math. 49, 2, 493–504.
• McKee, J.F. and Smyth, C. J. (2004) Salem numbers of trace −2 and traces of totally positive algebraic integers. Lecture Notes in Comput. Sci., 3076, Springer-Verlag, Berlin, 327-337.
• McKee, J.F. and Smyth, C. J. (2005) There are Salem numbers of every trace. Bull. London Math. Soc. 37, 1, 25–36.
• McKee, J. F. (2011) Computing totally positive algebraic integers of small trace. Math. Comp. 80, 274, 1041–1052.
• Smyth, C. J. (1984) The mean value of totally real algebraic numbers. Math. Comp. 42, 166, 663–681.
• Smyth, C. (2015) Seventy years of Salem numbers. Bull. Lond. Math. Soc. 47, 3, 379–395.