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Original Articles

On the Structure and Slopes of Drinfeld Cusp Forms

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References

  • Bandini, A., Valentino, M. (2018). On the Atkin Ut-operator for Γ1(t)-invariant Drinfeld cusp forms. Int. J. Number Theory. 14(10): 2599–2616.
  • Bandini, A., Valentino, M. (2019). On the Atkin Ut-operator for Γ0(t)-invariant Drinfeld cusp forms. Proc. Amer. Math. Soc. 147(10): 4171–4187.
  • Böckle, G. An Eichler-Shimura isomorphism over function fields between Drinfeld modular forms and cohomology classes of crystals. Avaliable at: www1.iwr.uni-heidelberg.de/groups/arith-geom/home/members/gebhard-boeckle/publications/.
  • Buzzard, K. (2001). Families of modular forms. Journal de Théorie Des Nombres de Bordeaux. 13(1): 43–52.
  • Buzzard, K., Calegari, F. (2004). A counterexample to the Gouvêa-Mazur conjecture. C.R. Acad. Sci. Paris, Ser. I. 338(10): 751–753.
  • Coleman, R. (1996). Classical and overconvergent modular forms. Invent. Math. 124(1-3): 215–241.
  • Coleman, R., Edixhoven, B. (1998). On the semi-simplicity of the Up-operator on modular forms. Math. Ann. 310(1): 119–127.
  • Cornelissen, G. (1997). A survey of Drinfeld modular forms, in [16], 167–187.
  • David, K. S., Webb, W. A. (1990). Lucas’ Theorem for prime powers. Europ. J. Combinatorics. 11: 188–196.
  • Fresnel, J., van der Put, M. (1981). Géométrie Analytique Rigide et Applications. Progress in Mathematics, vol. 18. Boston: Birkhäuser.
  • Gekeler, E. U. (1980). Drinfeld Modular Curves. Lecture Notes in Mathematics, vol. 1231. Berlin: Springer-Verlag.
  • Gekeler, E. U. (1988). On the coefficients of Drinfeld modular forms. Invent. Math. 93(3): 667–700.
  • Gekeler, E. U. (1995). Improper Eisenstein series on Bruhat-Tits trees. Manuscripta Math. 86(1): 367–391.
  • Gekeler, E. U. (1997). On the Drinfeld discriminant function. Comput. Math. 106(2): 181–202.
  • Gekeler, E. U., Nonnengardt, U. (1995). Fundamental domains of some arithmetic groups over function fields. Int. J. Math. 6(5): 689–708.
  • Gekeler, Ed E.U., van der Put, M., Reversat, M., van Geel, J. (1997). Drinfeld Modules, Modular Schemes and Applications. Proceedings of the workshop held in Alden-Biesen, September 9–14, 1996. River Edge, NJ: World Scientific Publishing Co., Inc.
  • Goss, D. (1980). Modular forms for Fr[T]. J. Reine Angew. Mat. 31, 16–39.
  • Goss, D. π¯-adic Eisenstein series for function fields. Compos. Math. 41 (1980), 3–38.
  • Goss, D. (2014). A construction of v-adic modular forms. J. Number Theory. 136: 330–338.
  • Gouvêa, F., Mazur, B. (1992). Families of modular eigenforms. Math. Comput. 58(198): 793–805.
  • Granville, A. (1997). Arithmetic Properties of Binomial Coefficients I: Binomial coefficients modulo prime powers. Canadian Mathematical Society Conference Proceedings 20, 253–275.
  • Hattori, S. Table of t-adic slopes on Drinfeld modular forms. Available at: http://www.comm.tcu.ac.jp/∼shinh/.
  • Hattori, S. Dimension variation of Gouvêa-Mazur type for Drinfeld cusp forms of level Γ1(t), to appear in Int. Math. Res. Not. Available at: https://doi.org/https://doi.org/10.1093/imrn/rnz104
  • Hattori, S. ℘-adic continuous families of Drinfeld eigenforms of finite slope. arXiv:1904.08618. [math.NT] (2019)
  • Hida, H. (1986). Galois representations into GL2(Zp〚X〛) attached to ordinary cusp forms. Invent. Math. 85(3): 545–613.
  • Hida, H. (1986). Iwasawa modules attached to congruences of cusp forms. Ann. Sci. École Norm. Sup. (4). 19(2): 231–273.
  • Hida, H., Maeda, Y. (1997). Non-abelian base change for totally real fields. Pacific J. Math. 181(3): 189–217. Olga Taussky-Todd: in memoriam.
  • Koblitz, N. (1984). p-Adic Numbers, p-Adic Analysis, and Zeta-Functions. GTM 58, New York: Springer-Verlag.
  • Nicole, M.-H., Rosso, G. (2019). Familles de formes modulaires de Drinfeld pour le groupe général linéaire. arXiv:1805.08793v3. [math.NT]
  • Petrov, A. (2013). A-expansion of Drinfeld modular forms. J. Number Theory. 133(7):2247–2266.
  • Serre, J.-P. (1973). Formes Modulaires et Fonctions Zeta p-Adiques. Modular forms in one variable III, Lecture Notes in Mathematics, vol. 350, Berlin: Springer Verlag.
  • Serre, J. P. (1980). Trees. Berlin, New York: Springer-Verlag.
  • Teitelbaum, J. T. (1991). The Poisson kernel for Drinfeld modular curves. J. Amer. Math. Soc. 4(3): 491–511.
  • Vincent, C. (2014). On the trace and norm maps from Γ0(m) to GL2(A). J. Number Theory. 142: 18–43.
  • Wolfram Research, Inc. (2014). Mathematica, Version 10.0. Champaign, Illinois: Champaign, IL.

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