Summary
An algebra given by quadratic relations in a polynomial algebra on infinite set of generators is introduced. Using it, we prove some explicit formulas for the coefficients of the Sturm sequence of a polynomial. In the second part we discuss a numerical example of polynomials studied by Euler. There, the Hilbert matrices and the Cauchy determinants appear in the asymptotics of the Sturm sequence.
2000 Mathematics Subject Classifications: 12D10, 16S37, 47B35
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A Yuri Ivanovich Manin, à l’occasion de son 70-ème anniversaire
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Ogievetsky, O., Schechtman, V. (2009). Une Algèbre Quadratique Liée à la Suite de Sturm. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 270. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4747-6_21
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DOI: https://doi.org/10.1007/978-0-8176-4747-6_21
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