Trivial points on towers of curves

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1. Abramovich. D., A linear lower bound on the gonality of modular curves, International Math. Res. Notices 20 (1996), 1005–1011. Zbl0878.14019MR1422373
2. Baker, M., Specialization of Linear Systems from Curves to Graphs, Algebra and Number Theory 2, no. 6 (2008), 613–653. Zbl1162.14018MR2448666
3. Baker, M., Norine, S., Riemann-Roch and Abel-Jacobi Theory on a Finite Graph, Advances in Mathematics, 215 (2007), 766–788. Zbl1124.05049MR2355607
4. Bekka, B., de la Harpe, P., Valette, A., Kazhdan’s property (T), New Mathematical Monographs, 11, Cambridge University Press, 2008. Zbl1146.22009MR2415834
5. Bourgain, J., Gamburd, A.Expansion and random walks in $S{L}_d(\mathbb{Z}/p^n\mathbb{Z})$:I, J. Eur. Math. Soc. 10, (2008), 987–1011. Zbl1193.20059MR2443926
6. Bourgain, J., Gamburd, A.Expansion and random walks in $S{L}_d(\mathbb{Z}/p^n\mathbb{Z})$: II, J. Eur. Math. Soc. 11, 1057–1103 (2009) Zbl1193.20060MR2538500
7. Brooks, R., On the angles between certain arithmetically defined subspaces of ${ℂ}^n$, Annales Inst. Fourier 37 (1987), 175–185. Zbl0611.15003MR894565
8. Burger, M., Estimations de petites valeurs propres du laplacien d’un revêtement de variétés riemanniennes compactes, C.R. Acad. Sc. Paris 302 (1986), 191–194. Zbl0585.53035MR832070
9. Cadoret, A., Tamagawa, A., Uniform boundedness of p-primary torsion of abelian schemes, Invent. Math., 188 (2012), 83–125. Zbl1294.14011MR2897693
10. Çiperiani, M., Stix, J., Weil-Châtelet divisible elements in Tate-Shafarevich groups, arXiv:1106.4255. Zbl1327.11040
11. Diaconis, P., Saloff-Coste, L., Comparison Techniques for Random Walk on Finite Groups, Ann. Probab. 21, no. 4 (1993), 2131–2156. Zbl0790.60011MR1245303
12. Dinai, O., Poly-log diameter bounds for some families of finite groups, Proc. Amer. Math. Soc. 134 (2006), 3137–3142. Zbl1121.05058MR2231895
13. Dinai, O.Diameters of Chevalley groups over local rings, arXiv:1201.4686. Zbl1263.20050MR3000421
14. Ellenberg, J., Hall, C., Kowalski, E., Expander graphs, gonality and variation of Galois representations, Duke Math. J. 161, no. 4 (2012), 1233–1275. Zbl1262.14021MR2922374
15. Faltings, G., Endlichkeitssätze für abelsche Variatäten über Zahlkörpern, Invent. math. 73 (1983), 349–366. Zbl0588.14026MR718935
16. Faltings, G., Diophantine approximation on abelian varieties, Annals of Math. 133 (1991), 549–576. Zbl0734.14007MR1109353
17. Frey, G., Curves with infinitely many points of fixed degree, Israel J. Math. 85 (1994), no. 1-3, 79–83. Zbl0808.14022MR1264340
18. Fried, M. D., Introduction to modular towers: generalizing dihedral group-modular curve connections, in Recent developments in the inverse Galois problem (Seattle, WA, 1993), 111-171, Contemp. Math., 186, Amer. Math. Soc., Providence, RI, 1995. Zbl0957.11047MR1352270
19. González-Jiménez, E., Xarles, X., On symmetric square values of quadratic polynomials, Acta Arithmetica 149, 145–159 (2011). Zbl1243.11046
20. González-Jiménez, E., Xarles, X., Five squares in arithmetic progression over quadratic fields, to appear in Rev. Mat. Iberoamericana. Zbl06260624MR2590593
21. Hindri, M., Silverman, J.H., Diophantine Geometry, An introduction. Graduate Texts in Mathematics 201. Springer-Verlag, New York, 2000. Zbl0948.11023MR1745599
22. Lang, S., Tate, J., Principal homogeneous spaces over abelian varieties, Amer. J. Math. 80, (1958), 659–684. Zbl0097.36203MR106226
23. Lazarsfeld, R., Lectures on Linear Series, With the assistance of Guillermo Fernández del Busto. IAS/Park City Math. Ser., 3, Complex algebraic geometry (Park City, UT, 1993), 161-219, Amer. Math. Soc., Providence, RI, 1997. Zbl0906.14002MR1442523
24. Li, P. and Yau, S.T., A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces Invent. math. 69 (1982), 269–291. Zbl0503.53042MR674407
25. Lubotzky, A., Discrete groups, expanding graphs and invariant measures, Progress in Math. 125, Birkaüser 1994. Zbl0826.22012MR1308046
26. Manin, Y., A uniform bound for p-torsion in elliptic curves, Izv. Akad. Nauk. CCCP 33, (1969), 459–465. Zbl0191.19601
27. Merel, L., Bornes pour la torsion des courbes elliptiques sur les corps de nombres, Invent. Math. 124 (1996), no. 1-3, 437–449. Zbl0936.11037MR1369424
28. Mohar, B., Eigenvalues, diameter, and mean distance in graphs, Graphs Combin. 7 (1991) 53–64. Zbl0771.05063MR1105467
29. Poonen, B.Gonality of modular curves in characteristic p, Math. Res. Lett. 14 (2007), no. 4, 691–701. Zbl1138.14016MR2335995
30. Silverman, J.H., The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 106, Springer-Verlag, 1986. Zbl0585.14026MR817210
31. Silverman, J.H., The Arithmetic of Dynamical Systems, Graduate Texts in Mathematics 241, Springer-Verlag, 2007. Zbl1130.37001MR2316407
32. Xarles, X.Squares in arithmetic progression over number fields, J. Number Theory 132 (2012) 379–389. Zbl1280.11037MR2875345
33. Zograf, P.Small eigenvalues of automorphic Laplacians in spaces of cusp forms, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 134 (1984), 157-168; translation in Journal of Math. Sciences 36, Number 1, 106–114. Zbl0536.10018MR741858