Nikolaev, Igor V. Foliations on modular curves. (English) Zbl 1417.11037 Bull. Braz. Math. Soc. (N.S.) 48, No. 1, 85-92 (2017). Summary: It is proved, that a foliation on a modular curve given by the vertical trajectories of holomorphic differential corresponding to the Hecke eigenform is either the Strebel foliation or the pseudo-Anosov foliation. Cited in 1 Document MSC: 11F12 Automorphic forms, one variable 11F11 Holomorphic modular forms of integral weight 57R30 Foliations in differential topology; geometric theory Keywords:Hecke eigenforms; singular foliations PDFBibTeX XMLCite \textit{I. V. Nikolaev}, Bull. Braz. Math. Soc. (N.S.) 48, No. 1, 85--92 (2017; Zbl 1417.11037) Full Text: DOI arXiv References: [1] Borevich, Z.I., Shafarevich, I.R.: Number Theory. Academic Press, New York (1966) · Zbl 0145.04902 [2] Casson, A.J., Bleiler, S.A.: Automorphisms of surfaces after Nielsen and Thurston. Lond. Math. Soc. Student Texts 9, Cambridge (1988) · Zbl 0649.57008 [3] Darmon, H.: Rational points on modular elliptic curves. CBMS Regional Conference Series 101. Amer. Math. Soc, Providence, RI (2004) [4] Diamond, F., Shurman, J.: A First Course in Modular Forms, GTM 228. Springer, Berlin (2005) · Zbl 1062.11022 [5] Lawson, H.B.: Foliations. Bull. Amer. Math. Soc. 80, 369-418 (1974) · Zbl 0293.57014 · doi:10.1090/S0002-9904-1974-13432-4 [6] Strebel, K.: Quadratic Differentials. Springer, Berlin (1984) · Zbl 0547.30001 · doi:10.1007/978-3-662-02414-0 [7] Thurston, W.P.: On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. 19, 417-431 (1988) · Zbl 0674.57008 · doi:10.1090/S0273-0979-1988-15685-6 [8] Veech, W.A.: Gauss measures for transformations on the space of interval exchange maps. Ann. Math. 115(2), 201-242 (1982) · Zbl 0486.28014 · doi:10.2307/1971391 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.