Geodesic
On the analytic complexity of discriminants
Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 86-101.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the notion of analytic complexity introduced by V. K. Beloshapka. We give an algorithm which allows one to check whether a bivariate analytic function belongs to the second class of analytic complexity. We also provide estimates for the analytic complexity of classical discriminants and introduce the notion of analytic complexity of a knot. 
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V. A. Krasikov; T. M. Sadykov. On the analytic complexity of discriminants. Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 86-101. http://geodesic.mathdoc.fr/item/TRSPY_2012_279_a7/

[1] Vitushkin A. G., “13-ya problema Gilberta i smezhnye voprosy”, UMN, 59:1 (2004), 11–24 | DOI | MR | Zbl

[2] Adams C. C., The knot book: An elementary introduction to the mathematical theory of knots, Freeman, New York, 1994 | MR | Zbl

[3] Bank S. B., Kaufman R. P., “A note on Hölder's theorem concerning the Gamma function”, Math. Ann., 232 (1978), 115–120 | DOI | MR | Zbl

[4] Beloshapka V. K., “Analytic complexity of functions of two variables”, Russ. J. Math. Phys., 14:3 (2007), 243–249 | DOI | MR | Zbl

[5] Beukers F., Heckman G., “Monodromy for the hypergeometric function $_nF_{n-1}$”, Invent. math., 95 (1989), 325–354 | DOI | MR | Zbl

[6] Gelfand I. M., Kapranov M. M., Zelevinsky A. V., Discriminants, resultants, and multidimensional determinants, Birkhäuser, Boston, 1994 | MR | Zbl

[7] Grothendieck A., “Esquisse d'un programme (Sketch of a programme)”, Geometric Galois actions, v. 1, LMS Lect. Note Ser., 242, Around Grothendieck's “Esquisse d'un programme”, Cambridge Univ. Press, Cambridge, 1997, 5–48, 243–283 | MR | Zbl

[8] Ostrowski A., “Über Dirichletsche Reihen und algebraische Differentialgleichungen”, Math. Z., 8 (1920), 241–298 | DOI | MR | Zbl

[9] Passare M., Sadykov T., Tsikh A., “Singularities of hypergeometric functions in several variables”, Compos. math., 141:3 (2005), 787–810 | DOI | MR | Zbl

[10] Zupan A., Bridge and pants complexities of knots, E-print, 2011, arXiv: 1110.3019[math.GT] | MR