Gouvêa, Fernando Q.; Mazur, Barry Searching for \(p\)-adic eigenfunctions. (English) Zbl 0851.11031 Math. Res. Lett. 2, No. 5, 515-536 (1995). Let \(U\) denote the Atkin operator. The authors propose a computational procedure to search for nonclassical overconvergent \(p\)-adic \(U\)-eigenforms. The idea is to approximate the \(p\)-adic \(U\)-eigenfunction expansion which eventually may produce a candidate Fourier expansion. They use the asymptotic \(U\)-spectral expansion to give concrete examples for \(p = 5,3\). Reviewer: A.Dabrowski (Szczecin) Cited in 2 ReviewsCited in 4 Documents MSC: 11F33 Congruences for modular and \(p\)-adic modular forms 11F30 Fourier coefficients of automorphic forms Keywords:overconvergent \(p\)-adic eigenforms; spectral expansion; Atkin operator; Fourier expansion PDFBibTeX XMLCite \textit{F. Q. Gouvêa} and \textit{B. Mazur}, Math. Res. Lett. 2, No. 5, 515--536 (1995; Zbl 0851.11031) Full Text: DOI