P-adic Banach Spaces and Families of Modular Forms
نویسندگان
چکیده
Let p be a prime, Cp the completion of an algebraic closure of the p-adicnumbers Qp and K a finite extension of Qp contained in Cp. Let v be the valuation on Cp such that v(p) = 1 and let | | be the absolute value on Cp such that |x| = p for x ∈ Cp. Suppose N is a positive integer prime to p. Let X1(Np) denote the modular curve over K which represents elliptic curves with Γ1(Np)-structure and let Up be the Hecke operator on modular forms on X1(Np) which takes a form with q-
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