℘-adic continuous families of Drinfeld eigenforms of finite slope

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Let p be a rational prime, vp the normalized p-adic valuation on Z, q>1 a power of p and A=Fq[t]. Let ℘∈A be an irreducible polynomial and n∈A a non-zero element which is prime to ℘. Let k≥2 and r≥1 be integers. We denote by Sk(Γ1(n℘r)) the space of Drinfeld cuspforms of level Γ1(n℘r) and weight k for Fq(t). Let n≥1 be an integer and a≥0 a rational number. Suppose that n℘ has an irreducible factor of degree one and the generalized eigenspace in Sk(Γ1(n℘r)) of slope a is one-dimensional. In this paper, under an assumption that a is sufficiently small, we construct a family {Fk′|vp(k′−k)≥logp⁡(pn+a)} of Hecke eigenforms Fk′∈Sk′(Γ1(n℘r)) of slope a such that, for any Q∈A, the Hecke eigenvalues of Fk and Fk′ at Q are congruent modulo ℘κ with some κ>pvp(k′−k)−pn−a.