Overconvergent modular form

In mathematics, overconvergent modular forms are elements of certain p-adic Banach spaces (usually infinite dimensional) containing classical spaces of modular forms as subspaces. They were introduced by Nicholas M. Katz in 1972.

References

• Robert F. Coleman Classical and Overconvergent Modular Forms (Invent. Math. 124 (1996))
• Robert F. Coleman, Classical and overconvergent modular forms. Les Dix-huitièmes Journées Arithmétiques (Bordeaux, 1993). J. Théor. Nombres Bordeaux 7 (1995), no. 1, 333--365. Zbl 1073.11515
• Robert F. Coleman Classical and Overconvergent Modular Forms of Higher Level, J. Theor. Nombres Bordeaux 9 (1997), no. 2, 395-403.
• Katz, Nicholas M. p-adic properties of modular schemes and modular forms. Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), pp. 69-190. Lecture Notes in Mathematics, Vol. 350, Springer, Berlin, 1973.

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